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Funar algebra $K_\infty=K_\infty(\alpha,\beta;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $\sigma_1^3-\alpha\sigma_1^2+\beta\sigma_1-...
We describe a presentation for the descent algebra of the symmetric group $\sym{n}$ as a quiver with relations. This presentation arises from a new construction of the descent algebra as a homomorphic...
If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebr...
The N-enlarged Galilei Hopf algebra is constructed. Its twist deformations are considered and the corresponding twisted space-times are derived.
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
As a continuation of \cite{HU}, we explore the submodule structures of the quantum divided power algebra $\mathcal{A}_q(n)$ introduced in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)...
In this note, one discusses about some varieties which are constructed analogously to the isospectral commuting varieties. These varieties are subvarieties of varieties having very simple desingulariz...
We study the C*-algebra of an affine map on a compact abelian group and give necessary and sufficient conditions for strong transitivity when the group is a torus. The structure of the C*-algebra is c...
In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of Newton's method. In t...
This is a joint work with Thomas Brustle. We study the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the indecomposable objects in C(S,M) as homotopy classes of curves in (...
The concept of modulation is generalized to pseudo-modulation and its subclassesincluding pre-modulation, generalized modulation and regular modulation. The moti- vation is to deˉne the valued analog...
Finding the singularity of a matrix is a basic problem in linear algebra. Chu and Schnitger first considered this problem in the communication complexity model, in which Alice holds the first half of ...
Abstract: We consider a q-analogue of the standard bilinear form on the commutative ring of symmetric functions. The q=-1 case leads to a Z-graded Hopf superalgebra which we call the algebra of odd sy...
Abstract: In this chapter, we survey the algebraic aspects of quantum Teichm\"uller space, generalized Kashaev algebra and a natural relationship between the two algebras.
Abstract: We study the relation between the instanton counting on ALE spaces and the BPS state counting on a toric Calabi-Yau three-fold. We put a single D4-brane on a divisor isomorphic to A_{N-1}-AL...

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