排序方式: 共有26条查询结果,搜索用时 78 毫秒
1.
Edward S. Letzter 《代数通讯》2013,41(4):1889-1893
2.
Edward S. Letzter 《Archiv der Mathematik》2017,109(6):499-503
We observe that a finitely generated algebraic algebra R (over a field) is finite dimensional if and only if the associated graded ring \({{\text {gr}}}{R}\) is right noetherian, if and only if \({{\text {gr}}}{R}\) has right Krull dimension, if and only if \({{\text {gr}}}{R}\) satisfies a polynomial identity. 相似文献
3.
Gail Letzter 《Journal of Algebra》1999,220(2):395
Let θ be an involution of a semisimple Lie algebra g, let gθ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct a quantum analog of U(gθ) which can be characterized as the unique subalgebra of the quantized enveloping algebra of g which is a maximal right coideal that specializes to U(gθ). 相似文献
4.
5.
We determine the structure of -free graphs with n vertices and minimum degree larger than : such graphs are homomorphic to the graph obtained from a -cycle by adding all chords of length , for some k. This answers a question of Messuti and Schacht. We deduce that the homomorphism threshold of -free graphs is 1/5, thus answering a question of Oberkampf and Schacht. 相似文献
6.
We study skew inverse power series extensions R[[y
− 1; τ, δ]], where R is a noetherian ring equipped with an automorphism τ and a τ-derivation δ. We find that these extensions share many of the well known features of commutative power series rings. As an application
of our analysis, we see that the iterated skew inverse power series rings corresponding to nth Weyl algebras are complete, local, noetherian, Auslander regular domains whose right Krull dimension, global dimension,
and classical Krull dimension are all equal to 2n. 相似文献
7.
Edward S. Letzter 《Algebras and Representation Theory》2003,6(1):47-70
Let G be a connected, simply connected complex semisimple Lie group of rank n. The deformations employed by Artin, Schelter and Tate, and Hodges, Levasseur and Toro can be applied to the single parameter quantizations, at roots of unity, of the Hopf algebra of regular functions on G. Each of the resulting complex multiparameter quantum groups F
,p
[G] depends on both a suitable root of unity and an antisymmetric bicharacter p: Z
n
×Z
n
C
×. These quantizations differ significantly from their single parameter (root-of-unity) counterparts, and, in particular, may have infinite-dimensional irreducible representations. Our approach to F
,p
[G] depends on a natural ×-action thereon, where is an n-torus, and our main result offers a classification of the primitive ideals: We use a multiparameter quantum Frobenius map to provide a bijection from (PrimF
,p
[G])/× onto G/H×H, where H is a maximal torus of G. In the single parameter case, this bijection is a consequence of work by De Concini and Lyubashenko, and De Concini and Procesi; our results require their analysis. Our methods also exploit earlier work by Moeglin and Rentschler concerning actions of algebraic groups on complex Noetherian algebras. In contrast to generic quantizations of the coordinate ring of G, the primitive spectrum of F
,p
[G] is not finitely stratified by the torus action. 相似文献
8.
We analyse the centralizer of the Macdonald difference operatorin an appropriate algebra of Weyl group invariant differenceoperators. We show that it coincides with Cherednik's commutingalgebra of difference operators via an analog of the Harish-Chandraisomorphism. Analogs of Harish-Chandra series are defined andrealized as solutions to the system of basic hypergeometricdifference equations associated to the centralizer algebra.These Harish-Chandra series are then related to both Macdonaldpolynomials and Chalykh's Baker–Akhiezer functions. 相似文献
9.
E. S. Letzter 《Proceedings of the American Mathematical Society》2007,135(1):1-4
Given an abelian category with arbitrary products, arbitrary coproducts, and a generator, we show that the closed subspaces (in the sense of A. L. Rosenberg) are parameterized by a suitably defined poset of ideals in the generator. In particular, the collection of closed subspaces is itself a small poset.
10.
Edward S. Letzter 《代数通讯》2013,41(7):2183-2190
Montgomery and Witherspoon proved that upper and lower semisolvable, semisimple, finite dimensional Hopf algebras are of Frobenius type when their dimensions are not divisible by the characteristic of the base field. In this note we show that a finite dimensional, semisimple, lower solvable Hopf algebra is always of Frobenius type, in arbitrary characteristic. 相似文献