Related papers: Non-integral central extensions of loop groups

We produce a partial compactification of the variety given by P(t)=N_{K/k}(\mathbf z) whose Brauer group coincides with the unramified Brauer group, where K is an \'etale k-algebra and P(t)\in k[t] is a nonconstant polynomial. Then we…

We prove that the maximum length of an irredundant base for a primitive action of a finite simple group of Lie type is bounded above by a function which is a polynomial in the rank of the group. We give examples to show that this type of…

The moduli space for a flat G-bundle over the two-torus is completely determined by its holonomy representation. When G is compact, connected, and simply connected, we show that the moduli space is homeomorphic to a product of two tori mod…

Let $ K / k $ be a purely inseparable extension of characteristic $ p> 0 $ and of finite size. We recall that $K/k$ is modular if for every $n \in \mathbb{N}$,$K^{p^n}$ and $k$ are $k\cap K^{p^ n}$-linearly disjoint. A natural…

This paper computes the obstruction to the existence of equivariant extensions of basic gerbes over non-simply connected compact simple Lie groups. By modifying a (finite dimensional) construction of Gaw\c{e}dzki-Reis [J. Geom. Phys.…

Let $k$ be a field of characteristic $0$, $X$ be a geometrically connected, smooth and proper variety over $k$ and $x\in X(k)$ be a base point. Using the notion of iterated universal extensions, we show that Nori's fundamental group…

A generalized Euler parameterization of a compact Lie group is a way for parameterizing the group starting from a maximal Lie subgroup, which allows a simple characterization of the range of parameters. In the present paper we consider the…

Let $R$ be a prime ring with center $Z(R)$ and with involution $*$. Given an additive subgroup $A$ of $R$, let $T(A):=\{x+x^*\mid x\in A\}$ and $K_0(A):=\{x-x^*\mid x\in A\}$. Let $L$ be a non-abelian Lie ideal of $R$. It is proved that if…

We introduce the $N=2$ Lie conformal superalgebras ${\frak {K}}(p)$ of Block type, and classify their finite irreducible conformal modules for any nonzero parameter $p$. where $p$ is a nonzero complex number. In particular, we show that…

For a number field $K$, a finite set of primes $S$ not containing a fixed prime $p$, we explain when extensions of group schemes of $\mu_p$ by $\Z/p\Z$ split over the ring of $S$-integers $O_S$ of $K$.

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together…

By a proper cover of a finite group G we mean an extension of a nontrivial finite group by G. Our purpose is to show that a proper cover of a finite simple group L of Lie type always contains an element whose order differs from the element…

A finite group $G$ is called $k$-factorizable if for every ordered factorization $|G|=a_1\cdots a_k$ into integers each greater than $1$ there exist subsets $A_1,\dots,A_k\subseteq G$ such that $|A_i|=a_i$ for each $i$ and $G=A_1\cdots…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

It is shown that in the units of augmentation one of an integral group ring $\mathbb{Z} G$ of a finite group $G$, a noncyclic subgroup of order $p^{2}$, for some odd prime $p$, exists only if such a subgroup exists in $G$. The corresponding…

A central extension is a regular epimorphism in a Barr exact category $\mathscr{C}$ satisfying suitable conditions involving a given Birkhoff subcategory of $\mathscr{C}$ (joint work with G. M. Kelly, 1994). In this paper we take…

We construct equivalences among four notions associated to a reductive group scheme $G$: factorization super central extensions of the loop group of $G$ by $\mathbb G_m$ subject to a condition on the commutator, factorization super line…

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our companion paper, establishing strongly…

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…