Geometric Analysis on H-type Groups Related to Division Algebras

Finite Dimensional Algebras, Quantum Groups and Finite Groups of Lie Type

We shall discuss generic extension monoids associated with finite dimensional (basic) hereditary algebras of finite or cyclic type and related applications to Ringel–Hall algebras, (and hence, to quantum groups). We shall briefly review the geometric setting of quantum gln by Beilinson, Lusztig and MacPherson and its connections to Ringel– Hall algebras and q-Schur algebras. In the second part ...

Classification, Automorphism Groups and Categorical Structure of the Two-Dimensional Real Division Algebras

The category of all 2-dimensional real division algebras is shown to split into four full subcategories each of which is given by the natural action of a Coxeter group of type A1 or A2 on the set of all pairs of ellipses in R which are centred in the origin and have reciprocal axis lengths. Cross-sections for the orbit sets of these group actions are being determined. They yield a classificatio...

Triangulaizability of Algebras Over Division Rings

Positive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

ON SELBERG-TYPE SQUARE MATRICES INTEGRALS

In this paper we consider Selberg-type square matrices integrals with focus on Kummer-beta types I & II integrals. For generality of the results for real normed division algebras, the generalized matrix variate Kummer-beta types I & II are defined under the abstract algebra. Then Selberg-type integrals are calculated under orthogonal transformations.