共查询到20条相似文献,搜索用时 31 毫秒
1.
Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices 总被引:1,自引:0,他引:1
Li Xia YE Zhi Xiang WU Xue Feng MEI 《数学学报(英文版)》2007,23(10):1729-1744
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d(y), which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d(y) and weak A-forms of wUq^d(y). 相似文献
2.
We classify the quadratic extensions and the finite groups G for which the group ring [G] of G over the ring of integers of K has the property that the group of units of augmentation 1 is hyperbolic. We also construct units in the ℤ-order of the quaternion algebra , when it is a division algebra. 相似文献
3.
V. D. Lyakhovsky 《Theoretical and Mathematical Physics》2006,148(1):968-979
In accordance with the quantum duality principle, the twisted algebra
is equivalent to the quantum group
and has two preferred bases: one inherited from the universal enveloping algebra
and the other generated by coordinate functions of the dual Lie group
. We show howthe transformation
can be explicitly obtained for any simple Lie algebra and a factorable chain
of extended Jordanian twists. In the algebra
, we introduce a natural vector grading
, compatible with the adjoint representation of the algebra. Passing to the dual-group coordinates allows essentially simplifying
the costructure of the deformed Hopf algebra
, considered as a quantum group
. The transformation
can be used to construct new solutions of the twist equations. We construct a parameterized family of extended Jordanian
deformations
and study it in terms of
; we find new realizations of the parabolic twist.
Dedicated to the birthday of my teacher, Yurii Novozhilov
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 112–125, July, 2006. 相似文献
4.
Let
and
be adjoint nilpotent orbits in a real semisimple Lie algebra. Write
≥
if
is contained in the closure of
. This defines a partial order on the set of such orbits, known as the closure ordering. We determine this order for the split
real form of the simple complex Lie algebra, E
8. The proof is based on the fact that the Kostant-Sekiguchi correspondence preserves the closure ordering. We also present
a comprehensive list of simple representatives of these orbits, and list the irreeducible components of the boundaries
and of the intersections
. 相似文献
5.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献
6.
Dorothee Schueth 《Geometriae Dedicata》2004,105(1):77-83
A nonflat Einstein solvmanifold (
, g) is said to be of standard type if in the associated metric Lie algebra
, the orthogonal complement
of the derived algebra is Abelian. It is an open question whether the standard condition is automatically satisfied for all
nonflat Einstein solvmanifolds. We derive certain properties of the metric Lie algebra
of a nonflat Einstein solvmanifold (
, g) under the assumption
. In particular, we obtain some new sufficient conditions which imply standard type. 相似文献
7.
We define the Hopf algebra structure on the Grothendieck group of finite-dimensional polynomial representations of
in the limitN→∞. The resulting Hopf algebra Rep
is a tensor product of its Hopf subalgebras Repa
,a ∈ ℂ×/q2ℤ. Whenq is generic (resp.,q
2 is a primitive root of unity of orderl), we construct an isomorphism between the Hopf algebra Rep
a
and the algebra of regular functions on the prounipotent proalgebraic group
(resp.,
). Whenq is a root of unity, this isomorphism identifies the Hopf subalgebra of Rep
a
spanned by the modules obtained by pullback with respect to the Frobenius homomorphism with the algebra generated by the
coefficients of the determinant of an element of
considered as anl×l matrix over the Taylor series. This gives us an explicit formula for the Frobenius pullbacks of the fundamental representations.
In addition, we construct a natural action of the Hall algebra associated to the infinite linear quiver (resp., the cyclic
quiver withl vertices) on Rep
a
and describe the span of tensor products of evaluation representations taken at fixed points as a module over this Hall algebra. 相似文献
8.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
9.
Amol Sasane 《Complex Analysis and Operator Theory》2009,3(1):323-330
Let E be a separable infinite-dimensional Hilbert space, and let denote the algebra of all functions that are holomorphic. If is a subalgebra of , then using an algebraic result of Corach and Larotonda, we derive that under some conditions, the Bass stable rank of is infinite. In particular, we deduce that the Bass (and hence topological stable ranks) of the Hardy algebra , the disk algebra and the Wiener algebra are all infinite.
Submitted: October 10, 2007., Revised: January 11, 2008., Accepted: January 12, 2007. 相似文献
10.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献
11.
Victor I. Lomonosov Heydar Radjavi Vladimir G. Troitsky 《Integral Equations and Operator Theory》2008,60(3):405-418
An algebra of operators on a Banach space X is said to be transitive if X has no nontrivial closed subspaces invariant under every member of the algebra. In this paper we investigate a number of
conditions which guarantee that a transitive algebra of operators is “large” in various senses. Among these are the conditions
of algebras being localizing or sesquitransitive. An algebra is localizing if there exists a closed ball B ∌ 0 such that for every sequence (x
n
) in B there exists a subsequence and a bounded sequence (A
k
) in the algebra such that converges to a non-zero vector. An algebra is sesquitransitive if for every non-zero z ∈ X there exists C > 0 such that for every x linearly independent of z, for every non-zero y ∈ X, and every there exists A in the algebra such that and ||Az|| ≤ C||z||. We give an algebraic version of this definition as well, and extend Jacobson’s density theorem to algebraically sesquitransitive
rings.
The second and the third authors were supported by NSERC. 相似文献
12.
John W. Snow 《Algebra Universalis》2008,58(1):59-71
We prove that if is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con contains a copy of an order polynomially complete lattice other than , , or Con, then Con is not hereditary.
Received March 7, 2006; accepted in final form December 5, 2006. 相似文献
13.
Harald Meyer 《Archiv der Mathematik》2008,90(2):112-122
Let p be a prime, G a finite group with p | |G| and F a field of characteristic p. By we denote the F-subspace of the centre of the group ring FG spanned by the p-regular conjugacy class sums. J. Murray proved that is an algebra, if G is a symmetric or alternating group. This can be used for the computation of the block idempotents of FG. We proved that is an algebra if the Sylow-p-subgroups of G are abelian. Recently, Y. Fan and B. Külshammer generalized this result to blocks with abelian defect groups. Here, we show
that is an algebra if the Sylow-2-subgroups of G are dihedral. Therefore and are algebras for all primes p and all prime powers q. Furthermore we prove that is an algebra for the simple Suzuki-groups Sz(q), where q is a certain power of 2 and p is an arbitrary prime dividing |Sz(q)|.
Received: 18 May 2007 相似文献
14.
G. E. Arutyunov L. O. Chekhov S. A. Frolov 《Theoretical and Mathematical Physics》1997,111(2):536-562
It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra
of the algebra of functions on the cotangent bundle over the centrally extended current group in two dimensions. It is governed
by two dynamic τ and
-matrices satisfying a closed system of equations. The corresponding quantum R- and
-matrices are found as solutions to quantum analogues of these equations. We present the quantum L-operator algebra and show
that the system of equations for R and
arises as the compatibility condition for this algebra. It turns out that the R-matrix is twist-equivalent to the Felder
elliptic RF-matrix, with
playing the role of the twist. The simplest representation of the quantum L-operator algebra corresponding to the elliptic
Ruijsenaars-Schneider model is obtained. The connection of the quantum L-operator algebra to the fundamental relation RB LL=LLRB with the Belavin elliptic R-matrix is established. As a by-product of our construction, we find a new N-parameter elliptic
solution to the classical Yang-Baxter equation.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 2, pp. 182–217, May, 1997. 相似文献
15.
We give a uniform interpretation of the classical continuous Chebyshev and Hahn orthogonal polynomials of a discrete variable
in terms of the Feigin Lie algebra
for λ∈ℂ. The Chebyshev and Hahn q-polynomials admit a similar interpretation, and orthogonal polynomials corresponding to
Lie superalgebras can be introduced. We also describe quasi-finite modules over
, real forms of this algebra, and the unitarity conditions for quasi-finite modules. Analogues of tensors over
are also introduced.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 205–236, May, 2000. 相似文献
16.
For an algebra
with an action of a Hopf algebra
we establish the pairing between equivariant cyclic cohomology and equivariant K-theory for
. We then extend this formalism to compact quantum group actions and show that equivariant cyclic cohomology is a target space
for the equivariant Chern character of equivariant summable Fredholm modules. We prove an analogue of Julg's theorem relating
equivariant K-theory to ordinary K-theory of the C*-algebra crossed product, and characterize equivariant vector bundles on quantum homogeneous spaces. 相似文献
17.
It is known [KRS] that for each finitely generated Banach algebra
there exists a numberN such that for eachn>N the matrix algebras
can be generated by three idempotents. In this paper we show that the same statement is true for direct sums
and
, where
is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for
algebras
because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra
can be generated by two idempotents if and only ifn
j
=2 for eachj and
is singly generated. Also we give an example of a free singly generated algebra
for which
can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x%
fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde
{\cal B}}\] can be generated by three idempotents for each singly generated free algebra
. 相似文献
18.
A. M. Semikhatov 《Theoretical and Mathematical Physics》1997,112(2):949-987
We review several constructions that are realized in bosonic and N = 2 strings and which relate the affine Lie algebra
(2), affine superalgebra
(2|1), and the superconformal N = 2 algebra.
This paper was written at the request of the Editorial Board.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 2, pp. 195–240, August, 1997. 相似文献
19.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献
20.
T. V. Skrypnyk 《Theoretical and Mathematical Physics》2008,155(1):633-645
Using the R-operator on a Lie algebra
satisfying the modified classical Yang-Baxter equation, we define two sets of functions that mutually commute with respect
to the initial Lie-Poisson bracket on
. We consider examples of the Lie algebras
with the Kostant-Adler-Symes and triangular decompositions, their R-operators, and the corresponding two sets of mutually
commuting functions in detail. We answer the question for which R-operators the constructed sets of functions also commute
with respect to the R-bracket. We briefly discuss the Euler-Arnold-type integrable equations for which the constructed commutative
functions constitute the algebra of first integrals.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 147–160, April, 2008. 相似文献