Algebra Seminar: Hu -- Lie Theory in the Higher Verlinde Category and Superalgebras in Characteristic Two

Serina Hu (MIT) will be speaking in the algebra seminar.  We will go out for lunch after
the talk---all are welcome to join! 

When: 12-1pm Friday March 21 

Where: Carslaw 175 

Title: Lie Theory in the Higher Verlinde Category and Superalgebras in Characteristic
Two (tentative title)

Abstract: The simplest nontrivial higher Verlinde category, Ver_4^+, is a reduction of
the category of supervector spaces to characteristic 2 (Venkatesh), so studying Lie
theory in this category provides a theory of supergroups and superalgebras in
characteristic 2.  In this talk, we first discuss representations of general linear
groups in Ver_4^+, which can be viewed as a notion of general linear supergroups in
characteristic 2.  We classify their irreducible representations in terms of highest
weights and conjecture a Steinberg tensor product theorem.  We then define a Lie algebra
in Ver_4^+ and prove a PBW theorem, which provides a notion of Lie superalgebra in
characteristic 2, and discuss how to classify such Lie algebras.  Finally, we define the
notion of Lie superalgebra in Ver_4^+, which will unify both a pre-existing notion of
Lie superalgebra in characteristic 2 as a Z/2-graded Lie algebra with squaring map
(Bouarroudj et.  al) and the notion of a Lie algebra in Ver_4^+.  Time permitting, we
will also discuss a natural lift of this notion to characteristic 0 (for perfect k),
which we call a mixed Lie superalgebra over a ramified quadratic extension of the ring
of Witt vectors W(k).  This is joint work with Pavel Etingof.