Semisimple algebras of almost minimal rank over the reals

Authors:
Markus Bläser;Andreas Meyer de Voltaire
Affiliations:
Computer Science Department, Saarland University;Chair of Information Technology and Education, ETH Zurich
Venue:
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Year:
2007

Citing 6
Cited 0

On associative algebras of minimal rank

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Algebraic Complexity Theory

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Abstract

A famous lower bound for the bilinear complexity of the multiplication in associative algebras is the Alder-Strassen bound. Algebras for which this bound is tight are called algebras of minimal rank. After 25 years of research, these algebras are now well understood. We here start the investigation of the algebras for which the Alder-Strassen bound is off by one. As a first result, we completely characterize the semisimple algebras over R whose bilinear complexity is by one larger than the Alder-Strassen bound.