共查询到20条相似文献,搜索用时 46 毫秒
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A. I. Kornev 《Siberian Mathematical Journal》2007,48(5):857-862
We continue studying the associative rings complete and reduced in the sense of Martynov. We prove that the group of invertible elements of a reduced associative ring is reduced. We compute the complete radical of a group ring over the ring of integers and the complete radical of the group algebra over an arbitrary algebra over a finite prime field. 相似文献
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V. Linchenko 《代数通讯》2013,41(6):1834-1851
We prove that, if H is a finite-dimensional semisimple Hopf algebra, and A is an FCR H-module algebra over an algebraically closed field, then A is a PI-algebra, provided the subalgebra of invariants is a PI-algebra. We also show that if A is an affine algebra with an action of a finite group G by automorphisms, the subalgebra of the fixed points AG is in the center of A, and the characteristic of the ground field is either zero or relatively prime to the order of G, then AG is affine. Analogous results are proved for graded algebras and H-module algebras over a semisimple triangular Hopf algebra over a field of characteristic zero. We prove also that, if A is an H-module algebra with an identity element, and H is either a semisimple group algebra or its dual, then, if A is semiprimitive (semiprime), then so is AH. 相似文献
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Selene Sánchez-Flores 《Journal of Pure and Applied Algebra》2012,216(3):718-733
We prove that the Gerstenhaber bracket on the Hochschild cohomology of the group algebra of a cyclic group over a field of positive characteristic is not trivial. In this case, we relate the Lie algebra structure on the odd degrees of the Hochschild cohomology with a Witt-type algebra. 相似文献
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A. R. Kemer 《Mathematical Notes》2012,92(3-4):375-382
We prove that any nonzero ideal of the group algebra of the infinite symmetric group over a field of nonzero characteristic contains skew-symmetric and symmetric elements of sufficiently large order. Using this result, we reduce the question of the classification of the ideals of the group algebra of the infinite symmetric group to the classification of certain subspaces of the tensor square of a finitely generated free associative algebra. 相似文献
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Automorphism groups of Weyl-type algebras 总被引:2,自引:0,他引:2
Let F be a field of characteristic 0, be n commuting variables over F, and be the field of all rational functions. Let . We have the simple Weyl type algebra . In this paper, the automorphism group of the associative algebra and the automorphism group of the Lie algebra are determined,
and it is proved that .
Received: 4 October 2001 / Revised version: 5 November 2001 相似文献
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Alexandr Usnich 《Advances in Mathematics》2011,228(4):1863
The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a noncommutative algebra that is an analog of a noncommutative field of two independent variables and prove that the Cremona group embeds in a group of outer automorphisms of this algebra. We give two proofs of it, the first proof is technical, the second one is conceptual and proceeds through a construction of a birational invariant of an algebraic variety from its bounded derived category of coherent sheaves. 相似文献
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整表代数是群代数的推广,它的理想是群代数码的推广.本文给出了整表代数的单边理想是自正交理想的必要充分条件. 相似文献
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Let Ψ be a field, G a finite group of automorphisms of Ψ, and Φ the fixed field of G. Let H be a Hopf algebra over Ψ. For g ∈ G we define a Hopf algebra Hg which has the same underlying vector space as H and modified operations and show that the tensor product (over Ψ) ?g ∈ G Hg has a Φ-form. As a consequence we see that if n>0 is an integer and Φ is a field of characteristic zero or p>0 with (n,p)=1, then there is a finite dimensional Hopf algebra over Φ with antipode of order 2n. 相似文献
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N. A. Koreshkov 《Russian Mathematics (Iz VUZ)》2010,54(9):30-35
In this paper, we describe finite-dimensional homogeneously simple algebras of associative type whose 1-component is a full
matrix algebra. In addition, we prove that a finite-dimensional division ring of associative type over an algebraically closed
field is isomorphic to a group algebra. 相似文献
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Derivations and Automorphisms of the Positive Part of the Two-parameter Quantum Group Ur,s(B3) 下载免费PDF全文
We compute the derivations of the positive part of the two-parameter quantum group U_(r,s)(B_3) and show that the Hochschild cohomology group of degree 1 of this algebra is a threedimensional vector space over the base field C. We also compute the groups of(Hopf) algebra automorphisms of the augmented two-parameter quantized enveloping algebra ?_(r,s)~(≥0)(B_3). 相似文献
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Shilin Yang 《Frontiers of Mathematics in China》2007,2(2):305-316
The group of Hopf algebra automorphisms for a finite-dimensional semisimple cosemisimple Hopf algebra over a field k was considered by Radford and Waterhouse. In this paper, the groups of Hopf algebra automorphisms for two classes of pointed
Hopf algebras are determined. Note that the Hopf algebras we consider are not semisimple Hopf algebras.
相似文献
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YU XiaoLan & LU DiMing 《中国科学 数学(英文版)》2011,(7)
Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well. 相似文献
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Nonlinearity of the Automorphism Groups of Some Free Algebras 总被引:2,自引:2,他引:0
We prove that the groups of tame automorphisms of a free Lie algebra (free associative algebra, absolutely free algebra, algebra of polynomials) of rank at least four over a field of characteristic zero admit no faithful representation by matrices over any field. 相似文献
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David R. Finston 《manuscripta mathematica》1987,58(1-2):229-244
In [5] it was shown that a finite dimensional binary algebra without nilpotents over an algebraically closed field of characteristic zero has only the trivial derivation and, consequently, a finite automorphism group. It is shown here that an m-ary algebra without nilpotents has only finitely many endomorphisms, with no assumptions on the characteristic of the base field. An upper bound on the dimension of the algebraic set of endomorphisms of a finite dimensional m-ary algebra, depending on the dimension of a maximal null subalgebra, is obtained if the base field is the complex field. The null subalgebras arising from a single derivation are examined for the case of an algebraically closed base field of characteristic zero. 相似文献
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We consider polynomial identities of group algebras over a field F of characteristic zero. We prove that any PI group algebra satisfies the same identities as a matrix algebra M n (F ), where n is the maximal degree of finite dimensional representations of the group over algebraic extensions of F. 相似文献
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We prove that any projective Schur algebra over a field K isequivalent in Br(K) to a radical abelian algebra. This was conjecturedin 1995 by Sonn and the first author of this paper. As a consequence,we obtain a characterization of the projective Schur group bymeans of Galois cohomology. The conjecture was known for algebrasover fields of positive characteristic. In characteristic zerothe conjecture was known for algebras over fields with a Henselianvaluation over a local or global field of characteristic zero. 相似文献
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Group codes are right or left ideals in a group algebra of a finite group over a finite field. Following the ideas of a paper on binary group codes by Bazzi and Mitter in 2006, we prove that group codes over finite fields of any characteristic are asymptotically good. 相似文献