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Mathematics Colloquium


Date:  Tuesday, January 21, 2014

Title:  Axial algebras of Jordan type

Abstract:  In an associative algebra, the adjoint endomorphism of an idempotent has minimal polynomial dividing x(x-1). In a nonassociative algebra, this need not be the case. We will discuss algebras that are minimally nonassociative in that they are commutative and generated by idempotents whose adjoint minimal polynomials divide x(x-1)(x-e), for some constant e. Jordan algebras occur in the case e=1/2, but the actual motivation for this work came from the Griess algebras of certain vertex operator algebras, where the cases e=1/4 and e=1/32 arise. Study of 2-generated subalgebras provides a classification theorem via Fischer's 3-transposition groups.

Speaker:  Jon Hall
Institution:  Michigan State University


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