Related papers: Fundamental Groups of Commuting Elements in Lie Gr…
In this paper, we describe the total space $E_{com} U(3)$ of the principal $U(3)$-bundle associated with the classifying space for commutativity $B_{com} U(3)$ as a homotopy colimit of a diagram of spaces and offer a computation of the mod…
Let $c:SU(n)\rightarrow PSU(n)=SU(n)/\mathbb{Z}_{n}$ be the quotient map of the special unitary group $SU(n)$ by its center subgroup $\mathbb{Z}_{n}$. We determine the induced homomorphism $c^{\ast}:$ $H^{\ast}(PSU(n))\rightarrow…
We will determine the motivic cohomology $H^{*,*}(BSO_n , Z/2)$ with coefficients in $Z/ 2$ of the classifying space of special orthogonal groups $SO_n$ over the complex numbers $C$.
Let $G$ be the classical group, and let Hom$(\mathbb{Z}^m,G)$ denote the space of commuting $m$-tuples in $G$. First, we refine the formula for the Poincar\'e series of Hom$(\mathbb{Z}^m,G)$ due to Ramras and Stafa by assigning (signed)…
We explicitly compute the first and second cohomology groups of the classical Lie superalgebras $sl_{m|n}$ and $osp_{2|2n}$ with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second…
Quantum Steiffel manifolds were introduced by Vainerman and Podkolzin in \cite{VP}. They classified the irreducible representations of their underlying $C^*$-algebras. Here we compute the K groups of the quantum homogeneous spaces…
Studies the cohomology of p-central, powerful, p-groups with a certain extension property. These groups are naturally associated to Lie algebras. The paper develops a machinery that calculates the first few terms of the Bockstein spectral…
We investigate the commuting automorphisms of nilpotent Lie algebras $L$ with coclass $\leq 3$. Our examination exposes the conditions under which the set of commuting automorphisms of $L$ forms a subgroup within its automorphism group.
The first and second homology groups are computed for configuration spaces of framed three-dimensional point particles with annihilation included, when up to two particles and an antiparticle are present.
We compute the first and second cohomology groups with coefficients in the adjoint module of frobeniusian model algebras whose parameters move in a dense open subset of $\mathbb{C}^{p-1}$, and obtain upper bounds for the dimension of…
In this paper, we obtain classification of the topological holonomy groups in $SO(3)$. Such a group is given by one of the following: a finite group (such groups are classified by Klein); a commutative infinite group which is generated by…
Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the…
Quantum spaces with $\frak{su}(2)$ noncommutativity can be modelled by using a family of $SO(3)$-equivariant differential $^*$-representations. The quantization maps are determined from the combination of the Wigner theorem for $SU(2)$ with…
We prove the following criterion for the pro-representability of the deformation cohomology of a commutative formal Lie group. Let f be a flat and separated morphism between noetherian schemes. Assume that the target of f is flat over the…
We study the commutator subgroup of integral orthogonal groups belonging to indefinite quadratic forms. We show that the index of this commutator is 2 for many groups that occur in the construction of moduli spaces in algebraic geometry, in…
Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…
The complex Lie group GO(2n,C) by definition consists of all complex matrices A of size 2n, such that A times transpose(A) is a non-zero scalar. In this paper we determine explicitly the singular cohomology ring of the classifying space…
A review of the characterization of principal bundles, through the different properties of the action of a group and its related canonical and translation maps, is presented. The work is divided in three stages: a topological group acting…
In this paper, first we give the controlling algebra of Lie triple systems. In particular, the cohomology of Lie triple systems can be characterized by the controlling algebra. Then using controlling algebras, we introduce the notions of…
Let $BPU(n)$ be the classifying space of the projective unitary group $PU(n)$. We determine the integral cohomology ring of $BPU(4)$, and the Steenrod algebra structure of its mod $2$ cohomology.