Algebra seminar in Lincoln on 20 January 2016: talk by Dr Gunnar Traustason

Charlotte Scott Centre for Algebra

will give a talk Symplectic Alternating Algebras and their groups of automorphisms at the Algebra seminar on 20 January 2016, Wednesday, at 4pm (room ENG209 in Engineering hub, building 13 on the uni map).

Abstract: A Symplectic Alternating Algebra is a symplectic vector space $latex L$, whose associated alternating form is nondegenerate, that is furthermore equipped with a binary alternating product with the extra requirement that $latex (xy,z)=(yz,x)$.

These linear structures originate from a study of powerful 2-Engel groups and there is a 1-1 correspondence between a rich class of powerful 2-Engel 3-groups of exponent 27 and Symplectic Alternating Algebras over the field of 3 elements.

We will give an overview of these and then focus on a recent result that states that any finite group can be realised as the automorphism group of some Symplectic Alternating Algebra.

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