Related papers: The compact exceptional Lie algebra $\mathfrak g^c…

This is the third paper of a series relating the equivariant twisted $K$-theory of a compact Lie group $G$ to the ``Verlinde space'' of isomorphism classes of projective lowest-weight representations of the loop groups. Here, we treat…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…

Let $R := R_{2}(p)=\mathbb{C}[t^{\pm 1}, u : u^2 = t(t-\alpha_1)\cdots (t-\alpha_{2n})] $ be the coordinate ring of a nonsingular hyperelliptic curve and let $\mathfrak{g}\otimes R$ be the corresponding current Lie algebra. \color{black}…

Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic…

We study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E_r^{*,*}[g] is defined for any Lie algebra g which models the Bockstein spectral sequence of the…

Let $\mathbf{c}_0$ be the lowest generalized two-sided cell of an extended affine Weyl group W. We determine the structure of the based ring of $\mathbf{c}_0$. For this we show that certain conjectures of Lusztig on generalized cells…

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…

We study a new class of infinite dimensional Lie algebras, which has important applications to the theory of integrable equations. The construction of these algebras is very similar to the one for automorphic functions and this motivates…

Let $\mathfrak g$ be a semisimple Lie algebra, $\mathfrak h\subset\mathfrak g$ a reductive subalgebra such that $\mathfrak h^\perp$ is a complementary $\mathfrak h$-submodule of $\mathfrak g$. In 1983, Bogoyavlenski claimed that one obtains…

We study the relation between two special classes of Riemannian Lie groups $G$ with a left-invariant metric $g$: The Einstein Lie groups, defined by the condition $\operatorname{Ric}_g=cg$, and the geodesic orbit Lie groups, defined by the…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…

Graded contractions of the fine $\mathbb{Z}_2^3$-grading on the complex exceptional Lie algebra $\mathfrak{g}_2$ are classified up to equivalence and up to strongly equivalence. In particular, a large family of 14-dimensional Lie algebras…

In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…

Let $\Gamma$ be a finite group acting on a simple Lie algebra $\mathfrak{g}$ and acting on a $s$-pointed projective curve $(\Sigma, \vec{p}=\{p_1, \dots, p_s\})$ faithfully (for $s\geq 1$). Also, let an integrable highest weight module…

In this short note, we construct an exotic example of a locally compact group $G$ with a Borel $2$-cocycle $\omega$ such that the non-twisted group von Neumann algebra $L(G)$ is a factor, while the twisted group von Neumann algebra…

For the associative algebra $A(\mathfrak g)$ of an infinite-dimensional Lie algebra $\mathfrak g$, we introduce twisted fiber bundles over arbitrary compact topological spaces. Fibers of such bundles are given by elements of algebraic…

Let $G$ be an exceptional simple algebraic group over an algebraically closed field $k$ and suppose that the characteristic $p$ of $k$ is a good prime for $G$. In this paper we classify the maximal Lie subalgebras $\mathfrak{m}$ of the Lie…

We present a special and attractive basis for the exceptional Lie algebra $G_2$, which turns $G_2$ into a $\mathbb{Z}_2^3$-graded Lie algebra. There are two basis elements for each degree of $\mathbb{Z}_2^3\setminus\{(0,0,0)\}$, thus…

We prove that the twisted group C*-algebra of a finitely generated nilpotent group is $\mathcal{Z}$-stable if and only if it is nowhere scattered, a condition that we characterize in terms of the given group and 2-cocycle. As a main…