Abstract
The notion of Hadamard decomposition of a semisimple associative finite-dimensional complex algebra generalizes the notion of classical Hadamard matrix corresponding to the case of commutative algebras. The algebras admitting a Hadamard decomposition are referred to as Hadamard algebras. We study the conjecture claiming that, if aHadamard algebra is not simple and has an irreducible character of degree m ≥ 2, then the dimension of the algebra is not less than 2m2. The validity of this conjecture is confirmed for the first two values m = 2and m = 4(here m must be even). Moreover, we prove a result (which is weaker than the conjecture) in which 2m2 is replaced by m2 + 2m.
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.
