相关论文: Equivariant K-groups of spheres with actions of in…

We show that $U(k)$-invariant hypercomplex structures on (open subsets) of regular semisimple adjoint orbits in $\mathfrak{gl}(k,{\mathbb C})$ correspond to algebraic curves $C$ of genus $(k-1)^2$, equipped with a flat projection…

We associate with each simple Lie algebra a system of second-order differential equations invariant under a non-compact real form of the corresponding Lie group. In the limit of a contraction to a Schr\"odinger algebra, these equations…

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…

Let $RG$ be the group ring of a finite group $G$ over a commutative ring $R$ with $1$. An element $x$ in $RG$ is said to be skew-symmetric with respect to an involution $\sigma$ of $RG$ if $\sigma(x)=-x.$ A structure theorem for the…

Let G be a split simple group of type G_2 over a field k, and let g be its Lie algebra. Answering a question of Colliot-Th\'el\`ene, Kunyavski\u{i}, Popov, and Reichstein, we show that the function field k(g) is generated by algebraically…

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of…

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact Lie group…

We generalize the Li-Yang notion of self-similar $k$-graph $(G,\Lambda)$ and its $C^*$-algebra $\mathcal{O}_{G,\Lambda}$ to any finitely aligned $k$-graph $\Lambda$. We then introduce an inverse semigroup model for $\mathcal{O}_{G,\Lambda}$…

Equipping a non-equivariant topological E_\infty operad with the trivial G-action gives an operad in G-spaces. The algebra structure encoded by this operad in G-spectra is characterised homotopically by having no non-trivial multiplicative…

In this paper we construct infinitely many examples of a Riemannian submersion from a simple, compact Lie group $G$ with bi-invariant metric onto a smooth manifold that cannot be a quotient of $G$ by a group action. This partially addresses…

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about $G$-invariant vector fields and one-forms are shown.

We study Wick-rotations of left-invariant metrics on Lie groups, using results from real GIT (\cite{1}, \cite{2}, \cite{3}). An invariant for Wick-rotation of Lie groups is given, and we describe when a pseudo-Riemannian Lie group can be…

For any abelian compact Lie group $G$, we introduce a family of $G$-stratified pseudomanifolds, whose main feature is the preservation of the orbit spaces in the category of stratified pseudomanifolds. Which generalize a previous definition…

We show that two approaches to equivariant strict deformation quantization of C*-algebras by actions of negatively curved Kahlerian Lie groups, one based on oscillatory integrals and the other on quantizations maps defined by dual…

We consider the semi-direct products $G=\mathbb Z^2\rtimes GL_2(\mathbb Z), \mathbb Z^2\rtimes SL_2(\mathbb Z)$ and $\mathbb Z^2\rtimes\Gamma(2)$ (where $\Gamma(2)$ is the congruence subgroup of level 2). For each of them, we compute both…

We compute the $RO(G)$-graded equivariant algebraic $K$-groups of a finite field with an action by its Galois group $G$. Specifically, we show these $K$-groups split as the sum of an explicitly computable term and the well-studied…

Using the Hopf superalgebra structure of the enveloping algebra $U(\mathfrak g)$ of a Lie superalgebra $\mathfrak=\mathrm{Lie}(G)$, we give a purely algebraic treatment of $K$-bi-invariant functions on a Lie supergroup $G$, where $K$ is a…

In this paper we define complex equivariant K-theory for actions of Lie groupoids using finite-dimensional vector bundles. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite equivariant…

Let $G$ be a finite group acting linearly on the vector space $V$ over a field of arbitrary characteristic. The action is called {\em coregular} if the invariant ring is generated by algebraically independent homogeneous invariants and the…

We investigate left-invariant ${\rm G}_2^*$-structures on 7-dimensional Lie groups, focusing on those whose holonomy algebras are indecomposable and of type III, the latter meaning that the socle of the holonomy representation is maximal.…