The five exceptional simple Lie algebras over the complex number are included one within
the other as $\mathfrak {g} _2\subset\mathfrak {f} _4\subset\mathfrak {e} _6\subset\mathfrak …

Axial algebras are a class of non-associative commutative algebras whose properties are
defined in terms of a fusion law. When this fusion law is graded, the algebra has a naturally …

This article is survey of recent developments in, and a tutorial on, the approach to PP v.
N\mathbf P NP and related questions called geometric complexity theory (GCT). It is written …

These notes have been prepared for the Workshop on “(Non)-existence of complex
structures on S 6”, celebrated in Marburg in March, 2017. The material is not intended to be …

We classify N= 1 SVOAs with no free fermions and with bosonic subalgebra a simply
connected WZW algebra which is not of type E. The latter restriction makes the classification …

In this paper we treat faithful actions of simple algebraic groups on irreducible modules and
on the associated Grassmannian varieties. By explicit calculation, we show that in each …

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and
the hypersurface that it defines. We focus on geometric aspects that may be relevant for …

We study the problem of characterizing linear preserver subgroups of algebraic varieties,
with a particular emphasis on secant varieties and other varieties of tensors. We introduce a …

We prove that spin groups act generically freely on various spinor modules, in the sense of
group schemes and in a way that does not depend on the characteristic of the base field. As …

We give a construction that takes a simple linear algebraic group G over a field and
produces a commutative, unital, and simple non-associative algebra A over that field. Two …