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21.
Bangteng Xu 《代数通讯》2013,41(12):5249-5263
A problem that has been open for a long time is whether an automorphism of the center of the integral group ring of a finite group permutes the class sums. As a generalization, the similar problem for integral table algebras has also been studied in a few papers. In this paper we further the investigation of the problem for integral C-algebras and table algebras. We will first present some necessary and sufficient conditions under which an algebra isomorphism between integral C-algebras is monomial, and as an application, obtain a conceptual proof of the class sum correspondence theorem of group rings of finite groups. Then we prove that an algebra isomorphism compatible with degree maps between standard integral nilpotent table algebras over the ring of algebraic integers is exact. As a direct consequence, we get Hertweck's result [6] for finite nilpotent groups. An application to association schemes is also presented. 相似文献
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《代数通讯》2013,41(9):2921-2940
ABSTRACT An equivalent version of the Generalized Nakayama Conjecture states that any projective almost complete tilting module admits a finite number of non-isomorphic indecomposable complements. Motivated by this connection, we investigate the number of possible complements of projective almost complete tilting modules for some particular classes of Artin algebras, namely monomial algebras and algebras with exactly two simple modules. 相似文献
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We determine the multiplicity algebras and multiplicity modules of a p-monomial module. For a general p-group P, we find a sufficient and necessary condition for an endo-monomial P-module to be an endo-permutation P-module, and prove that a capped indecomposable endo-monomial P-module is of p ′-rank. At last, we give an alternative definition of the generalized Dade P-group. 相似文献
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Mohammed Tesemma 《代数通讯》2013,41(7):2258-2274
This article focuses on two recent results on multiplicative invariants of finite reflection groups: Lorenz (2001) showed that such invariants are affine normal semigroup algebras, and Reichstein (2003) proved that the invariants have a finite SAGBI basis. Reichstein (2003) also showed that, conversely, if the multiplicative invariant algebra of a finite group G has a SAGBI basis, then G acts as a reflection group. There is no obvious connection between these two results. We will show that multiplicative invariants of finite reflection groups have a certain embedding property that implies both results simultaneously. 相似文献
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In this paper, algebras are finite dimensional over an algebraically closed field k, and modules are k-finite dimensional left modules. We prove the stable equivalence conjecture for algebras stably equivalent to algebras A with the following conditions: basic, connected and selfinjective; rad3A = 0 but rad2A ¬ 0; and the separated quiver Q3 A of the quiver QA of A consisting of more than two connected components. 相似文献
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In this paper we give by a unified formula the classification of exceptional compact simple Kantor triple systems defined on tensor products of composition algebras corresponding to realifications of exceptional simple Lie algebras. 相似文献
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N. Gurappa Prasanta K. Panigrahi T. Shreecharan 《Journal of Computational and Applied Mathematics》2003,160(1-2):103-112
We elaborate upon a new method of solving linear differential equations, of arbitrary order, which is applicable to a wide class of single and multi-variate equations. Our procedure separates the operator part of the equation under study in to a part containing a function of the Euler operator and constants, and another one retaining the rest. The solution of the equation is then obtained from the monomials (or the monomial symmetric functions, for the multi-variate case), which are the eigenfunctions of the Euler operator. Novel exponential forms of the solutions of the differential equations enable one to analyze the underlying symmetries of the equations and explore the algebraic structures of the solution spaces in a straightforward manner. The procedure allows one to derive various properties of the orthogonal polynomials and functions in a unified manner. After showing how the generating functions and Rodriguez formulae emerge naturally in this method, we briefly outline the generalization of the present approach to the multi-variate case. 相似文献
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《代数通讯》2013,41(12):6115-6134
Abstract We give some techniques to determine the ideal K I generated by the monomials x k 1 y k 2 belonging to the integral closure ī of an ideal I ? ?{x, y}. We also give a sufficient condition for a weighted homogeneous ideal I ? ?{x, y} to satisfy the relation ī = I + K I . 相似文献