Abstract
In this paper, we present some results on algebraic complexity theory, which is a relatively new region of complexity theory. We consider the complexity of multiplication (bilinear complexity) in group algebras. In the 6-dimensional group algebra C(S3) over the field of complex numbers with permutations of the third order as the basis, we find a bilinear algorithm for multiplication with multiplicative complexity equal to 9 (instead of trivial 36) and prove that this bound is unimprovable. We prove a series of assertions on the structure of the group algebra C(S3), in particular, we show that the algebra C(S3) is decomposed into a direct product of the algebra of 2 × 2 matrices and two one-dimensional algebras.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
