Representations of solvable Lie algebras. II. Twisted group rings
نویسندگان
چکیده
منابع مشابه
On representations of twisted group rings
We generalize certain parts of the theory of group rings to the twisted case. Let G be a finite group acting (possibly trivially) on a field L of characteristic coprime to the order of the kernel of this operation. Let K ⊆ L be the fixed field of this operation, let S be a discrete valuation ring with field of fractions K, maximal ideal generated by π and integral closure T in L. We compute the...
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0. Introduction. 1. Let G be a group of linear transformations on a finite dimensional real or complex vector space X. Assume X is completely reducible as a G-module. Let 5 be the ring of all complexvalued polynomials on X, regarded as a G-module in the obvious way, and let J C 5 be the subring of all G-invariant polynomials on X. Now let J be the set of all ƒ £ J having zero constant term and ...
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1. Introduction. Let © be a Lie algebra over a field A. A decomposition of © is a triple (ni, b, n2) of subalgebras of © such that ® = niffif)©n2 a vector space direct sum and such that [b, n,-]Cn< for 4 = 1, 2. In [5] we showed how one could "induce" ©-modules from b-modules in a natural manner. In this paper we prove a useable necessary and sufficient condition that a ©-module must satisfy in...
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Several classifications of solvable Lie algebras of small dimension are known. Up to dimension 6 over a real field they were classified by G. M. Mubarakzjanov [Mubarakzjanov 63a, Mubarakzjanov 63b], and up to dimension 4 over any perfect field by J. Patera and H. Zassenhaus [Patera and Zassenhaus 90]. In this paper we explore the possibility of using the computer to obtain a classification of s...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 1975
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.1283