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A Lie group $G$ naturally acts on its Lie algebra $\gg$, called the adjoint action. In this paper, we determine the orbit types of the compact exceptional Lie group $G_2$ in its Lie algebra $\gg_2$. ...
We study qualitative properties of the group von Neumann algebra of a Baumslag-Solitar group. Namely, we prove that, in the non-amenable and {ICC} case, the associated ${\rm II}_1$ factor is prime, no...
We know that any element $X$ of the exceptional Jordan algebra $\gJ$ is transformed to a diagonal form by the compact exceptional Lie group $F_4$. However, its proof is used the method which is reduce...
We show a different modification of Poincare algebra that also preserves Lorentz algebra. The change begins with how boosts affect spacetime in a way similar to how they affect the momenta in kappa Po...
We obtain a description of the C*-algebras which can occur as a simple quotient of the C*-algebra of a locally injective surjection on a compact metric space of finite covering dimension.
We define a super version of the Connes-Moscovici Hopf algebra, $\mathcal{H}_1$. For that, we consider the supergroup $G^s=Diff^+(\mathbb{R}^{1,1})$ of orientation preserving diffeomorphisms of the s...
In this paper I consider the structure of the polylinear mapping of the free algebra over the commutative ring.
We introduce a new model for the secondary Steenrod algebra at the prime 2 which is both smaller and more accessible than the original construction of H.-J. Baues.
In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and...
Let $A_1:=K\langle x, \frac{d}{dx} \rangle$ be the Weyl algebra and $\mI_1:= K\langle x, \frac{d}{dx}, \int \rangle$ be the algebra of polynomial integro-differential operators over a field $K$ of cha...
The three integrable two-dimensional Henon-Heiles systems and their integrable perturbations are revisited. A family of new integrable perturbations is found, and N-dimensional completely integrable ...
For the algebra $\mI_1= K\langle x, \frac{d}{dx}, \int \rangle$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It i...
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the conce...
In this paper, we provide a uniform method to thoroughly classify all Harish-Chandra modules over some Lie algebras and superconformal algebras related to the Virasoro algebras. We first classify suc...
We study the Toeplitz algebra T (N ⋊ N×) and three quotients of this algebra: the C-algebra QN recntly introduced by Cuntz, and two new ones, which we call the additive and multiplicative bound...

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