Idempotents inducing a Z_2 grading on nonassociative algebras and their corresponding involutions.

Speaker
Yoav Segev (BGU)
Date
08/05/2016 - 13:00 - 12:00Add to Calendar 2016-05-08 12:00:00 2016-05-08 13:00:00 Idempotents inducing a Z_2 grading on nonassociative algebras and their corresponding involutions. Jordan algebras J of charateristic not 2 sometimes contain a set of idempotents (e^2=e) that generate J such that  their adjoint map ad_e: u \mapsto ue (u\in J) has the minimal polynomial x(x-1)(x-1/2), and with additional restrictions on products of elements in the eigenspaces of ad_e (for each e). Generalizing these properties (not only of such Jordan algebras) Hall, Rehren, Shpectorov (HRS) introduced ``Axial algebras of Jordan type''.  In my talk I will present structural results on Axial algebras of Jordan type 1/2 (a case which was not dealt with in HRS), I will discuss their idempotents e,  the corresponding ``Miyamoto involutions'' \tau(e) and the group that these involutions  generate. This is joint work with J. Hall, S. Shpectorov. seminar room אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
seminar room
Abstract

Jordan algebras J of charateristic not 2 sometimes contain
a set of idempotents (e^2=e) that generate J such that  their adjoint
map ad_e: u \mapsto ue (u\in J) has the minimal polynomial
x(x-1)(x-1/2), and with additional restrictions on products
of elements in the eigenspaces of ad_e (for each e).

Generalizing these properties (not only of such Jordan
algebras) Hall, Rehren, Shpectorov (HRS) introduced ``Axial algebras
of Jordan type''.  In my talk I will present structural results
on Axial algebras of Jordan type 1/2 (a case which was not
dealt with in HRS), I will discuss their idempotents e,  the corresponding
``Miyamoto involutions'' \tau(e) and the group that these involutions 
generate.

This is joint work with J. Hall, S. Shpectorov.

Last Updated Date : 08/05/2016