Related papers: On cubic action of a rank one group

We consider quantum group representations for a semisimple algebraic group G at a complex root of unity q. Here q is allowed to be of any order. We revisit some fundamental results of Parshall-Wang and Andersen-Polo-Wen from the 90's. In…

Let $\mathcal{O}_K$ be a complete discrete valuation ring with field of fractions $K$ and algebraically closed residue field $k.$ Let $G$ be a smooth connected commutative algebraic group over $K$ which does not contain a copy of…

Let G be an affine algebraic group and let X be an affine algebraic variety. An action $G\times X \to X$ is called observable if for any G-invariant, proper, closed subset Y of X there is a nonzero invariant $f\in K[X]^G$ such that f(Y) =0.…

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial finite dimensional irreducible rational $KG$-module.…

Let $K$ be an algebraic number field with ring of integers $\Cal{O}_{K}$, $p>2$ be a rational prime and $G$ be the cyclic group of order $p $. Let $\Lambda$ denote the order $\Cal{O}_{K}[G].$ Let $Cl(\Lambda)$ denote the locally free class…

We investigate rational $G$-modules $M$ for a linear algebraic group $G$ over an algebraically closed field $k$ of characteristic $p > 0$ using filtrations by sub-coalgebras of the coordinate algebra $k[G]$ of $G$. Even in the special case…

Let H_g denote the closed 3-manifold obtained as the connected sum of g copies of S^2 times S^1, with free fundamental group of rank g. We prove that, for a finite group G acting on H_g which induces a faithful action on the fundamental…

Let $G$ be a discrete countable infinite group. We show that each topological $(C,F)$-action $T$ of $G$ on a locally compact non-compact Cantor set is a free minimal amenable action admitting a unique up to scaling non-zero invariant Radon…

Consider $(G, V)$ a finite-dimensional representation of a connected reductive complex Lie group $G$ and $\mathbb{P}\left( V\right) $ the projective space of $V$. Denote by $G'$ the derived subgroup of $G$ and assume that the categorical…

We consider the model-theoretic Grothendieck ring of definable sets in ordered abelian groups. It is well-known that $\mathrm{K} \mathbb{Q} \cong \mathbb{Z}[T]/(T^2 + T)$ and $\mathrm{K} \mathbb{Z} =0$, but surprisingly little is known…

For a group $G$, N-series $\cal G$ of $G$ and commutative ring $R$ let $I^n_{R,\cal G}(G)$, $n\ge 0$, denote the filtration of the group algebra $R(G)$ induced by $\cal G$, and $I_R(G)$ its augmentation ideal. For subgroups $H$ of $G$, left…

While Jordan algebras are commutative, their non-associativity makes it so that the Jordan product operators do not necessarily commute. When the product operators of two elements commute, the elements are said to operator commute. In some…

We introduce a procedure based on computational algebraic geometry to determine whether two algebras are isomorphic. We then apply it to show that if $R$ is a commutative unital ring in which $2$ is not invertible, $G$ is a group of order…

A rational group of hermitian type is an algebraic group over the rational numbers whose symmetric space is a hermitian symmetric space. We assume such a group $G$ to be given, which we assume is isotropic. Then, for any rational parabolic…

We show that if G is a discrete group which does not have the Haagerup property but does have an unbounded cocycle into a C_0 representation and if G acts on a finite von Neumann algebra B such that the inclusion B \subset (B \rtimes G) has…

Let $G$ be a proper subgroup of $\mathbb{Q}$ and $S_G$ be the set of primes $p$ for which $G$ is $p$-divisible. We show that the model-theoretic Grothendieck ring of the ordered abelian group $(G;+,<)$ is a quotient of…

In this article, we show that every Jordan {g, h}-derivation over T_n(C) is a {g, h}-derivation under an assumption, where C is a commutative ring with unity 1 not equal to 0. We give an example of a Jordan {g, h}-derivation over T_n(C)…

The main aim of this paper is to prove $R$-triviality for simple, simply connected algebraic groups with Tits index $E_{8,2}^{78}$ or $E_{7,1}^{78}$, defined over a field $k$ of arbitrary characteristic. Let $G$ be such a group. We prove…

Let w be an elliptic element of the Weyl group of a connected reductive group G. Let X be the set of pairs (g,B) where g is an element of G, B is a Borel subgroup of G and B,gBg^{-1} are in relative position w. Then G acts naturally on X.…

Let $G$ be a finite group of order $n$, and $Z_G=\mathbb{Z}\langle\zeta_{i,g}\mid g\in G,\ i=1,2,\dots,n\rangle$ be the free generic algebra, with canonical action of $G$ according to $(\zeta_{i,g})^x=\zeta_{i,x^{-1}g}$. It is proved that…