Related papers: Anti-commuting varieties

Let $G$ be a simple algebraic group of type $F_{4}$, $E_{6}$, $E_{7}$ or $E_{8}$, and let $\mathfrak{g}$ be its Lie algebra. The adjoint variety $X_{ad} \subseteq \mathbb{P} \mathfrak{g}$ is defined as the unique closed orbit of the adjoint…

We investigate non-commutative differential calculus on the supersymmetric version of quantum space where the non-commuting super-coordinates consist of bosonic as well as fermionic (Grassmann) coordinates. Multi-parametric quantum…

We study compactifications of the moduli space of unordered points in the plane via variation of GIT quotients of their corresponding Hilbert scheme. Our VGIT considers linearizations outside the ample cone and within the movable cone. For…

We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing…

We define the associated variety $ X_{M} $ of a module $ M $ over a finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of the cone $ X $ of…

One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically,…

The first part of this paper deals with unipotent and reductive groups over finite fields with $q$ elements in which either $q$ goes to infinity or $G=GL_n(q)$ and $n$ goes to infinity. The second part of the paper deals with the symmetric…

The commuting graph of a semigroup is the set of non-central elements; the edges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example of a field $F$ and an integer $n$ such that the commuting graph of…

The paper contains three main results. First, we show that if a commutative semigroup variety is a modular element of the lattice Com of all commutative semigroup varieties then it is either the variety COM of all commutative semigroups or…

We study the GIT quotient of the symplectic grassmannian parametrizing lagrangian subspaces of \bigwedge^3{\mathbb C}^6 by the natural action of SL_6, call it M. This is a compactification of the moduli space of smooth double EPW-sextics.…

We describe absolute nilpotent and some idempotent elements of an $n$- dimensional evolution algebra corresponding to two permutations and we decompose such algebras to the direct sum of evolution algebras corresponding to cycles of the…

The condition of nilpotency is studied in the general linear Lie algebra $\mathfrak{gl}_{n}(\mathbb{K})$ and the symplectic Lie algebra $\mathfrak{sp}_{2m}(\mathbb{K})$ over an algebraically closed field of characteristic 0. In particular,…

Consider a compact prequantizable symplectic manifold M on which a compact Lie group G acts in a Hamiltonian fashion. The ``quantization commutes with reduction'' theorem asserts that the G-invariant part of the equivariant index of M is…

Using an algebraic orbifold method, we present non-commutative aspects of $G_2$ structure of seven dimensional real manifolds. We first develop and solve the non commutativity parameter constraint equations defining $G_2$ manifold algebras.…

When the action of a reductive group on a projective variety has a suitable linearisation, Mumford's geometric invariant theory (GIT) can be used to construct and study an associated quotient variety. In this article we describe how…

The purpose of this paper is to provide a way to compute the intersection cohomology of the GIT quotient of a nonsingular projective variety. We show that the middle perversity intersection cohomology of the GIT quotient $M//G$ is naturally…

We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective…

Let $G(\mathbb{R})$ be a real reductive group. Suppose $\pi$ is an irreducible representation of $G(\mathbb{R})$ having a Whittaker model, and consider three invariants of $\pi$ related to nilpotents elements of the Lie algebra of $G$ (or…

Let $G$ be a reductive group over an algebraically closed field of positive characteristic $p$, good for the root system of $G$. The closures of $G$-orbits in the Hilbert nullcone of the coadjoint representation are conical affine Poisson…

Let us consider the group $G = < x,y \mid x^m = y^n>$ with $m$ and $n$ nonzero integers. In this paper, we study the variety of epresentations $R(G)$ and the character variety $X(G)$ in $SL(2,\C)$ of the group $G$,obtaining by elementary…