Complexity of multiplication in commutative group algebras over fields of characteristic 0 |
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Authors: | B V Chokaev |
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Institution: | 1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia
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Abstract: | Let rkA denote the bilinear complexity (also known as rank) of a finite-dimension associative algebra A. Algebras of minimal rank are widely studied from the point of view of bilinear complexity. These are the algebras A for which the Alder-Strassen inequality is satisfied as an equality, i.e., rkA = 2dimA ? t, where t is the number of maximum two-sided ideals in A. It is proved in this work that an arbitrary commutative group algebra over a field of characteristic 0 is an algebra of minimal rank. The structure and precise values of the bilinear complexity of commutative group algebras over a field of rational numbers are obtained. |
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