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1.
For any increasing function which takes only finitely many distinct values, a connected finite dimensional algebra is constructed, with the property that for all ; here is the -generated finitistic dimension of . The stacking technique developed for this construction of homological examples permits strong control over the higher syzygies
of -modules in terms of the algebras serving as layers.
The first author was supported in part by a fellowship stipend from the National Physical Science Consortium and the National
Security Agency. The second author was partially supported by a grant from the National Science Foundation. 相似文献
2.
In this paper, we study and classify Hilbert space representations of cross product -algebras of the quantized enveloping algebra with the coordinate algebras of the quantum motion group and of the complex plane, and of the quantized enveloping algebra with the coordinate algebras of the quantum group and of the quantum disc. Invariant positive functionals and the corresponding Heisenberg representations are explicitly described.Presented by S.L. Woronowicz. 相似文献
3.
Piotr Mikołaj Sołtan 《Algebras and Representation Theory》2006,9(6):581-591
Given a discrete quantum group we construct a Hopf -algebra which is a unital -subalgebra of the multiplier algebra of . The structure maps for are inherited from and thus the construction yields a compactification of which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra.Partially supported by Komitet Badań Naukowych grants 2P03A04022 & 2P03A01324, the Foundation for Polish Science and Deutsche Forschungsgemeinschaft. 相似文献
4.
Dong Yang 《Algebras and Representation Theory》2009,12(1):63-75
By studying certain centralizer subalgebras of the affine Schur algebra we show that is Noetherian and we determine its center. Assuming n ≥ r, we show that is Morita equivalent to , and the Schur functor is an equivalence under certain conditions.
The author acknowledges support by National Natural Science Foundation of China No.10131010. 相似文献
5.
Let be a commutative Noetherian local ring and let be an ideal of R. We give some inequalities between the Bass numbers of an R–module and those of its local cohomology modules with respect to . As an application of these inequalities, we recover results of Delfino-Marley and Kawasaki by showing that for a minimax
R-module M and for any non-negative integer i, the Bass numbers of the ith local cohomology module are finite if one of the following holds:
S. Yassemi was supported by a grant from IPM No. 85130214. 相似文献
(a) | , |
(b) | is a principal ideal. |
6.
Alex S. Dugas 《Algebras and Representation Theory》2007,10(3):223-240
Over an Artin algebra Λ many standard concepts from homological algebra can be relativized with respect to a contravariantly
finite subcategory of mod-Λ, which contains the projective modules. The main aim of this article is to prove that the resulting relative homological
dimensions of modules are preserved by stable equivalences between Artin algebras. As a corollary, we see that Auslander’s
notion of representation dimension is invariant under stable equivalence (a result recently obtained independently by Guo).
We then apply these results to the syzygy functor for self-injective algebras of representation dimension three, where we
bound the number of simple modules in terms of the number of indecomposable nonprojective summands of an Auslander generator.
相似文献
7.
Christopher Kennedy 《Algebras and Representation Theory》2006,9(5):525-537
Deep matrix algebras based on a set over a ring are introduced and studied by McCrimmon when has infinite cardinality. Here, we construct a new -module that is faithful for of any cardinality. For a field of arbitrary characteristic and , is studied in depth. The algebra is shown to possess a unique proper non-zero ideal, isomorphic to . This leads to a new and interesting simple algebra, , the quotient of by its unique ideal. Both and the quotient algebra are shown to have centers isomorphic to . Via the new faithful representation, all automorphisms of are shown to be inner in the sense of Definition 18.Presented by D. Passman. 相似文献
8.
9.
Our aim is to construct new examples of totally ordered and ∗-ordered noncommutative integral domains. We will discuss the
following classes of rings: enveloping algebras U(L), group rings
G and smash products U(L)
G. All of them are examples of Hopf algebras. Characterizations of orderability for enveloping algebras and group rings and
of ∗-orderability for enveloping algebras have been found before and will be recalled in the article. Our main results are:
for and L finite–dimensional, we characterize the orderability of U(L)
G; for , we give a necessary and a sufficient condition for ∗-orderability of
G (G orderable, respectively, G residually ‘torsion-free nilpotent’). Moreover, for and L finite-dimensional, we reduce the problem of characterizing the ∗-orderability of U(L)
G to the problem of characterizing the ∗-orderability of
G. The latter remains open.
The research of the first author was supported by the Ministry of Education, Science and Sport of the Republic of Slovenia
under grant P1-0222 (Algebraic methods in operator theory). The research of the second and third author was supported by the
Natural Sciences and Engineering Research Council of Canada. 相似文献
10.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献
11.
Hideo Mitsuhashi 《Algebras and Representation Theory》2006,9(3):309-322
In this paper, we establish Schur–Weyl reciprocity between the quantum general super Lie algebra and the Iwahori–Hecke algebra . We introduce the sign -permutation representation of on the tensor space of dimensional -graded -vector space . This action commutes with that of derived from the vector representation on . Those two subalgebras of satisfy Schur–Weyl reciprocity. As special cases, we obtain the super case (), and the quantum case (). Hence this result includes both the super case and the quantum case, and unifies those two important cases.Presented by A. Verschoren. 相似文献
12.
In this paper, we consider a finite dimensional semisimple cosemisimple quasitriangular Hopf algebra with (we call this type of Hopf algebras almost-quasitriangular) over an algebraically closed field . We denote by the vector space generated by the left tensorand of . Then is a sub-Hopf algebra of . We proved that when is odd, has a triangular structure and can be obtained from a group algebra by twisting its usual comultiplication [14]; when is even, is an extension of an abelian group algebra and a triangular Hopf algebra, and may not be triangular. In general, an almost-triangular
Hopf algebra can be viewed as a cocycle bicrossproduct.
相似文献
13.
A. Ardizzoni 《Algebras and Representation Theory》2008,11(5):461-496
The construction of the cotensor coalgebra for an “abelian monoidal” category which is also cocomplete, complete and AB5, was performed in Ardizzoni et al. (Comm Algebra 35(1):25–70, 2007). It was also proved that this coalgebra satisfies a meaningful universal property which resembles the classical one. Here
the lack of the coradical filtration for a coalgebra E in is filled by considering a direct limit of a filtration consisting of wedge products of a subcoalgebra D of E. The main aim of this paper is to characterize hereditary coalgebras , where D is a coseparable coalgebra in , by means of a cotensor coalgebra: more precisely, we prove that, under suitable assumptions, is hereditary if and only if it is formally smooth if and only if it is the cotensor coalgebra if and only if it is a cotensor coalgebra , where N is a certain D-bicomodule in . Because of our choice, even when we apply our results in the category of vector spaces, new results are obtained.
This paper was written while A. Ardizzoni was member of G.N.S.A.G.A. with partial financial support from Mi.U.R. 相似文献
14.
Kohji Yanagawa 《Algebras and Representation Theory》2006,9(6):569-579
Let $E = K{\left\langle {y_{1} ,...,y_{n} } \right\rangle }Let be the exterior algebra. The (cohomological) distinguished pairs of a graded E-module N describe the growth of a minimal graded injective resolution of N. R?mer gave a duality theorem between the distinguished pairs of N and those of its dual N
*. In this paper, we show that under Bernstein–Gel’fand–Gel’fand correspondence, his theorem is translated into a natural corollary of local duality for (complexes of) graded -modules. Using this idea, we also give a -graded version of R?mer’s theorem.To the memory of Professor Tetsushi Ogoma. 相似文献
15.
The category of all two-dimensional real commutative division algebras is shown to split into two full subcategories. One
of them is equivalent to the category of the natural action of the cyclic group of order 2 on the open right half plane . The other one is equivalent to the category of the natural action of the dihedral group of order 6 on the set of all ellipses
in which are centered at the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions
are easily described. Together with they classify all real commutative division algebras up to isomorphism. Moreover we describe all morphisms between the objects
in this classifying set, thus obtaining a complete picture of the category of all real commutative division algebras, up to
equivalence. This supplements earlier contributions of Kantor and Solodovnikov, Hypercomplex Numbers: An Elementary Introduction to Algebras, Nauka, Moscow, 1973; Benkart et al., Hadronic J., 4: 497–529, 1981; and Althoen and Kugler, Amer. Math. Monthly, 90: 625–635, 1983, who achieved partial results on the classification of the real commutative division algebras.
Dedicated to Claus Michael Ringel on the occasion of his 60th birthday. 相似文献
16.
Let be a finite-dimensional hereditary algebra of finite or tame representation type over a finite field, and let be a rigid -module. Then the element in the Ringel–Hall algebra is an iterated skew commutator of the isoclasses of simple -modules. This gives a new characterization of the rigidness of an indecomposable module over a tame hereditary algebra.The first author was partially supported by a grant from the NSF; and the second author was supported by the Doctorial Foundation of the Ministry of Education of People’s Republic of China, and the NSFC (Grant No. 10271113 and 10301033). 相似文献
17.
T. Skrypnyk 《Acta Appl Math》2007,99(3):261-282
We construct a family of special quasigraded Lie algebras
of functions of one complex variables with values in finite-dimensional Lie algebra
, labeled by the special 2-cocycles F on
. The main property of the constructed Lie algebras
is that they admit Kostant-Adler-Symes scheme. Using them we obtain new integrable finite-dimensional Hamiltonian systems
and new hierarchies of soliton equations. 相似文献
18.
Csaba Szántó 《Algebras and Representation Theory》2006,9(5):465-495
We present formulas for the structure constants (Hall numbers) of the Hall algebra associated to the Kronecker algebra. The formulas which in some cases involve the classical Hall polynomials enable us to determine every Hall number. Using again these formulas we construct new PBW-bases with simple structure constants for the composition algebra , making possible the definition of the generic composition algebra via Hall polynomials.Presented by C. Ringel. 相似文献
19.
For a smashing localisation L of the derived category of a differential graded (dg) algebra A we construct a dg algebra A
L
and a morphism of dg algebras A→A
L
that induces the canonical map in cohomology. As a first application we obtain a localisations of a dg algebra A with graded commutative homology at a prime ideal in the homology H
*
A, namely a morphism of dg algebras. As a second application we can use results of Keller to “model” every smashing localisation of compactly
generated algebraic triangulated categories by a morphism of dg algebras.
相似文献
20.
We study relations between finite-dimensional representations of color Lie algebras and their cocycle twists. Main tools are the universal enveloping algebras and their FCR-properties (finite-dimensional representations are completely reducible.) Cocycle twist preserves the FCR-property. As an application, we compute all finite dimensional representations (up to isomorphism) of the color Lie algebra .Presented by A. Verschoren. 相似文献