Search arXivSearch

arXiv · 2208.01496

A survey of support theories for Lie superalgebras and finite supergroup schemes

Abstract

We survey the current state of various support variety theories for Lie superalgebras and finite supergroup schemes. We pay particular attention to the theory in characteristic zero developed by Boe, Kujawa, and Nakano using relative Lie superalgebra cohomology, and to the theory developed in positive characteristic in our previous work.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Christopher M. Drupieski, Jonathan R. Kujawa. 2022-08-02. A survey of support theories for Lie superalgebras and finite supergroup schemes. https://doi.org/10.1090/conm%2F804

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

On singular supports of Lusztig's perverse sheaves

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if and only if its singular support is contained in Lusztig's Lagrangian variety, that is, the variety of nilpotent representations of the preprojective algebra of the quiver.

math.RT

Skein algebras and quantized Coulomb branches

To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a one-holed torus, we describe a relationship between this quantized Coulomb branch and the Kauffman bracket skein algebra of the surface. We formulate a general conjecture relating these algebras.

math.RT

Kernel of Scott modules and Brauer indecomposability

Let $k$ be an algebraically closed field of prime characteristic $p$. Let $G$ be a finite group. We investigate the Brauer indecomposability of Scott $kG$-modules in relation to the kernel of modules. We generalize a criterion for Brauer indecomposability. We also prove that, in certain cases, Brauer indecomposability of a Scott $kG$-module can be lifted from that of a Scott module over a $p$-local subgroup.

math.RT