Bounds for Bilinear Complexity of Noncommutative Group Algebras

Details Bounds for Bilinear Complexity of Noncommutative Group Algebras Bounds for Bilinear Complexity of Noncommutative Group Algebras

2010-03-24

arxiv.org/abs/1003.4679v1

Computer Science

Computational Complexity

20 pages

Scientific paper

We study the complexity of multiplication in noncommutative group algebras which is closely related to the complexity of matrix multiplication. We characterize such semisimple group algebras of the minimal bilinear complexity and show nontrivial lower bounds for the rest of the group algebras. These lower bounds are built on the top of Bl\"aser's results for semisimple algebras and algebras with large radical and the lower bound for arbitrary associative algebras due to Alder and Strassen. We also show subquadratic upper bounds for all group algebras turning into "almost linear" provided the exponent of matrix multiplication equals 2.

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