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1.
A base of the universal multiplicative envelope for the free Malcev superalgebra on one odd generator is constructed. Some corollaries for central skew-symmetric elements in free Malcev and free alternative algebras are obtained. In particular, the Malcev Grassmann algebra is constructed. 相似文献
2.
The nucleus of a Malcev superalgebra M measures how far it is from being a Lie superalgebraM being a Lie superalgebra if and only if its nucleus is the whole M. This paper is devoted to study Malcev superalgebras in the opposite direction, that is, with trivial nucleus. The odd part of any finite-dimensional Malcev superalgebra with trivial nucleus is shown to be contained in the solvable radical. For algebraically closed fields, any such superalgebra splits as the sum of its solvable radical and a semisimple Malcev algebra contained in the even part, which is a direct sum of copies of sl(2, F) and the seven-dimensional simple non-Lie Malcev algebra, obtained from the Cayley-Dickson algebra. 相似文献
3.
Jiřrina Scholtzová 《代数通讯》2013,41(1):96-107
A base of the free alternative nil-superalgebra of index n, for n ≥ 3, on one odd generator is constructed. In particular, its index of solvability is computed. As a corollary over a field of characteristic zero an infinite family of solvable alternative algebras which are not associative of arbitrary big solvability index with explicit multiplication table is obtained. 相似文献
4.
Thequantumdouble(QD)theory['-3],whichwasfirstproposedbyDrinfeld[1],isaquitepowerfultoolinconstructingsolutionsofthequantumYang-Barerequations(QYBE).ThecoreoftiletheoryliesinthefaCtthatfromagivenHopf(super)ajgebraonecallgetauniquequasitriangularHopf(super)algebrawithauniversalRmatrix.Further,onemayobtainthenumericalsolutionsofQYBEbystudyingtherepresentations,especially,thefinite-dimensionalrepresentationsofQD.Thus,itisinterestingtoopennewwaysforconstructingQD's.Astepinthisdirectionhasb… 相似文献
5.
6.
The maximum matching graph M(G) of a graph G is a simple graph whose vertices are the maximum matchings of G and where two maximum matchings are adjacent in M(G) if they differ by exactly one edge. In this paper, we prove that if a graph is isomorphic to its maximum matching graph, then every block of the graph is an odd cycle. 相似文献
7.
Yu. Yu. Kochetkov 《Functional Analysis and Its Applications》2010,44(2):118-124
The cell structure of the spaces ℳ2,1 and ℳ3,1 is considered. These are the spaces of complex curves of genus 2 and 3 with one marked point. For the space ℳ2,1, nine cells of the highest dimension 8 are described and their adjacency is studied. For the space ℳ3,1, a list of all 1726 cells of the highest dimension 14 (with orientation) is obtained. The list of adjacent couples of cells
is also obtained. These lists can be found on the web. 相似文献
8.
E. Arthur Robinson 《Israel Journal of Mathematics》1986,56(1):75-88
This paper studies a spectral invariant ℳ
T
for ergodic measure preserving transformationsT called theessential spectral multiplicities. It is defined as the essential range of the multiplicity function for the induced unitary operatorU
T. Examples are constructed where ℳ
T
is subject only to the following conditions: (i) 1∈ℳ
T
, (ii) lcm(n, m)∈ℳ
T
wherevern, m ∈ ℳ
T
, and (iii) sup ℳ
T
<+∞. This shows thatD
T, definedD
T=card ℳ
T
, may be an arbitrary positive integer. The results are obtained by an algebraic construction together with approximation
arguments.
This research was partially supported by NSF grant MCS 8102790. 相似文献
9.
In this paper we consider operators acting on a subspace ℳ of the space L
2 (ℝm; ℂm) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace
ℳ is defined as the orthogonal sum of spaces ℳs,k of specific Clifford basis functions of L
2(ℝm; ℂm).
Every Clifford endomorphism of ℳ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic
operators are characterized in terms of commutation relations and they transform a space ℳs,k into a similar space ℳs′,k′. Hence, once the Clifford-Hermite-monogenic decomposition of an operator is obtained, its action on the space ℳ is known.
Furthermore, the monogenic decomposition of some important Clifford differential operators with polynomial coefficients is
studied in detail. 相似文献
10.
11.
LetR be a finite commutative ring with identity and τ be a nonnegative integer. In studying linear finite automata, one of the
basic problems is how to characterize the class of rings which have the property that every (weakly) invertible linear finite
automaton ℳ with delay τ over R has a linear finite automaton ℳ′ over R which is a (weak) inverse with delay τ of ℳ. The rings
and linear finite automata are studied by means of modules and it is proved that *-rings are equivalent to self-injective
rings, and the unsolved problem (for τ=0) is solved. Moreover, a further problem of how to characterize the class of rings
which have the property that every invertible with delay τ linear finite automaton ℳ overR has a linear finite automaton ℳ′ over R which is an inverse with delay τ′ for some τ′⩾τ is studied and solved.
Project supported by the National Natural Science Foundation of China(Grant No. 69773015). 相似文献
12.
Nathanaël Enriquez Jacques Franchi Yves Le Jan 《Probability Theory and Related Fields》2001,119(2):213-255
Let ℳ be a geometrically finite hyperbolic surface with infinite volume, having at least one cusp. We obtain the limit law
under the Patterson-Sullivan measure on T
1ℳ of the windings of the geodesics of ℳ around the cusps. This limit law is stable with parameter 2δ− 1, where δ is the Hausdorff
dimension of the limit set of the subgroup Γ of M?bius isometries associated with ℳ. The normalization is t
−1/(2δ−1), for geodesics of length t. Our method relies on a precise comparison between geodesics and diffusion paths, for which we need to approach the Patterson-Sullivan
measure mentioned above by measures that are regular along the stable leaves.
Received: 8 October 1999 / Revised version: 2 June 2000 / Published online: 21 December 2000 相似文献
13.
V. N. Zhelyabin 《Siberian Mathematical Journal》2018,59(6):1051-1062
Studying the unital simple Jordan superalgebras with associative even part, we describe the unital simple Jordan superalgebras such that every pair of even elements induces the zero derivation and every pair of two odd elements induces the zero derivation of the even part. We show that such a superalgebra is either a superalgebra of nondegenerate bilinear form over a field or a four-dimensional simple Jordan superalgebra. 相似文献
14.
S. A. Shakhova 《Algebra and Logic》2006,45(4):277-285
Let ℳ be any quasivariety of Abelian groups, Lq(ℳ) be a subquasivariety lattice of ℳ, dom
G
ℳ
be the dominion of a subgroup H of a group G in ℳ, and G/dom
G
ℳ
(H) be a finitely generated group. It is known that the set L(G, H, ℳ) = {dom
G
N
(H)| N ∈ Lq(ℳ)} forms a lattice w.r.t. set-theoretic inclusion. We look at the structure of dom
G
ℳ
(H). It is proved that the lattice L(G,H,ℳ) is semidistributive and necessary and sufficient conditions are specified for
its being distributive.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 484–499, July–August, 2006. 相似文献
15.
P. P. Kulish 《Journal of Mathematical Sciences》1991,54(3):923-930
A quantum deformation of the simplest rank-one orthosymplectic Lie superalgebra is constructed in two ways: by changing the anticommutatoin relations of the odd generators [V+, V–] ~ shH, and by using a constant triangular R-matrix which is an appropriate limit of the R-matrix of the supersymmetric sine-Gordon model. A relationship between these two approaches is established. The matrix elements of the odd generators and an analog of the Casimir operator are found for finite-dimensional representations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 95–106, 1988. 相似文献
16.
For the Kac-Moody superalgebra associated with the loop superalgebra with values in a finite-dimensional Lie superalgebra
g, we show what its quadratic Casimir element is equal to if the Casimir element for g is known (if g has an even invariant
supersymmetric bilinear form). The main tool is the Wick normal form of the even quadratic Casimir operator for the Kac-Moody
superalgebra associated with g; this Wick normal form is independently interesting. If g has an odd invariant supersymmetric
bilinear form, then we compute the cubic Casimir element. In addition to the simple Lie superalgebras g = g(A) with a Cartan
matrix A for which the Shapovalov determinant was known, we consider the Poisson Lie superalgebra poi(0|n) and the related
Kac-Moody superalgebra.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 378–397, September, 2008. 相似文献
17.
For a class ℳ of monomorphisms of a category, mathematicians consider different types of essentiality, depending on ℳ. In
this paper, considering the category of acts over a semigroup, we first briefly study the class ℳ
p
of a certain kind of pure monomorphisms, in a manner borrowed from V. Gould, to be called sequentially pure. Then, we study in detail three kinds of essentiality with respect to this class, and give some useful criteria to get (internal)
characterizations (in terms of elements) for essentialities. Finally, the relations between injectivity, essentiality, retractness,
and injective hulls, all with respect to the class of sequentially pure monomorphisms, are investigated.
The second author is thankful to Iran National Science Foundation (INSF) for their financial support. 相似文献
18.
If an algebraA is quantum commutative with respect to the action of a quasitriangular Hopf algebraH, then the monoidal structure on the categoryH
ℳ
of modules overH induces a rnonoidal structure on the categoryA#H
ℳ
of modules over the associated smash productA # H. The condition under which the braiding structure ofH
ℳ
induces a braiding structure onA#H
ℳ
is further investigated. Dually, the notion of quantum cocommutativity is introduced, and similar result in this dual situation
is obtained. 相似文献
19.
The extension space ℰ(ℳ) of an oriented matroid ℳ is the poset of all one-element extensions of ℳ, considered as a simplicial
complex. We present two different constructions leading to rank 4 oriented matroids with disconnected extension space. We
prove especially that if an elementf is not contained in any mutation of a rank 4 oriented matroid ℳ, then ℰ(ℳ\f) contains an isolated point. A uniform nonrealizable arrangement of pseudoplanes with this property is presented.
The examples described contrast results of Sturmfels and Ziegler [12] who proved that for rank 3 oriented matroids the extension
space has the homotopy type of the 2-sphere. 相似文献
20.
Simple right alternative superalgebras which have a simple algebra as even part and, as odd part, an irreducible bimodule over the even part are investigated. Under these conditions, superalgebras with one dimensional even part are classified, as well as superalgebras having M 2(F) as even part and a unital irreducible bimodule over M 2(F) of dimension less than or equal to 6 as odd part. It is shown that there is only a unique non alternative simple right alternative superalgebra of the first type and, for the second type, there is a infinite family depending on a single parameter. 相似文献