共查询到20条相似文献,搜索用时 15 毫秒
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David A. Craven 《Journal of Pure and Applied Algebra》2011,215(3):221-231
Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by the direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander-Reiten quiver. For dihedral 2-groups, we also show that there is at most one algebraic module on each component of the (stable) Auslander-Reiten quiver. We include a strong conjecture on the relationship between periodicity and algebraicity. 相似文献
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LetG be a finitep-group, and letU(G) be the group of units of the group algebraFG, whereF is a field of characteristicp. It is shown that, if the commutative subgroup ofG has order at leastp
2, then the nilpotency class ofU(G) is at least 2p−1.
The authors are grateful to the Dipartimento di Matematica of the Universita di Trento, and to the Mathematical Institute
of the University of Oxford, for their hospitality while this paper was being written. Then are also grateful to Robert Sandling,
for communication of results, and problems, prior to publication. 相似文献
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Aner Shalev 《Israel Journal of Mathematics》1990,70(3):257-266
The nilpotency class of the unit groupU of a modularp-group algebraFG is determined whenp is odd andG has a cyclic commutator subgroup. This is done via an extension of a theorem of Coleman and Passman, dealing with wreath
products obtained as sections ofU. 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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K. Erdmann 《Mathematische Zeitschrift》1990,203(1):321-334
Dedicated to B. Huppert on his 60th birthday 相似文献
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Thorsten Holm 《代数通讯》2013,41(6):1957-1969
Let k be a field of characteristic P >0 and let G be a finite abelian group. We determine the structure of the Hochschild cohomology ring of the group algebra k G. Moreover, we prove that for any finite group G the Krull dimension of H H *(k G) equals the p-rank of G. 相似文献
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The Auslander-Reiten quiver of a finite-dimensional associative algebra encodes information about the indecomposable finite-dimensional representations of and their homomorphisms. A component of the Auslander-Reiten quiver is called preprojective if it does not admit oriented cycles and each of its modules can be shifted into a projective module using the Auslander-Reiten translation. Preprojective components play an important role in the present research on algebras of finite and tame representation type. We present an algorithm which detects all preprojective components of a given algebra.
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Yu Qiu 《中国科学 数学(英文版)》2019,(7)
We survey various generalizations of braid groups for quivers with superpotential and focus on the cluster braid groups, which are introduced in a joint work with King(2018). Our motivations come from the study of cluster algebras, Calabi-Yau categories and Bridgeland stability conditions. 相似文献