This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2‎, ‎mathbb{Z}_p)$‎. ‎It then describes a natural base change map between the Iwasawa algebras or more correctly‎, ‎as it turns out‎, ‎between the global distribut...

A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed deformation parameter q ∈ C \ {0} exactness is proven for all q which are not a root of un...

We consider unital simple inductive limits of generalized dimension drop C∗-algebras They are so-called ASH-algebras and include all unital simple AH-algebras and all dimension drop C∗-algebras. Suppose that A is one of these C∗-algebras. We show that A ⊗ Q has tracial rank no more than one, where Q is the rational UHF-algebra. As a consequence, we obtain the following classification result: Le...

It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra representations can be classified, for non-generic q, by Young tableaux of the symmetric group due to the isomorphy of the group algebras for q → 1. Since spinors can ...

We consider Diagram algebras, DG(Q) (generalized Temperley-Lieb algebras) defined for a large class of graphs G, including those of relevance for cubic lattice Potts models, and study their structure for generic Q. We find that these algebras are too large to play the precisely analogous role in three dimensions to that played by the Temperley-Lieb algebras for generic Q in the planar case. We ...

In this paper we study a q-analogue of the convolution product on the line in detail. A convolution product on the braided line was defined algebraically by Kempf and Majid. We adapt their definition in order to give an analytic definition for the q-convolution and we study convergence extensively. Since the braided line is commutative as an algebra, all results can be viewed both as results in...

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equiva...

In this paper we first give a lower bound on multiplicities for Buchsbaum homogeneous k-algebras A in terms of the dimension d, the codimension c, the initial degree q, and the length of the local cohomology modules of A. Next, we introduce the notion of Buchsbaum k-algebras with minimal multiplicity of degree q, and give several characterizations for those rings. In particular, we will show th...

The notion of (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras is introduced. Some characterization theorems in (∈,∈ ∨q)-interval-valued fuzzy prime ideals in commutative BCK-algebras are derived. Also we study relation between (∈,∈ ∨q)-interval-valued fuzzy prime ideal and (∈ ∨q)-interval-valued fuzzy level prime ideals. Characterization of interval-valued fuzzy set to b...

A group completion functor Q is constructed in the category of algebras in simplicial sets over a cofibrant En-operad M. It is shown that Q defines a Bousfield–Friedlander simplicial model category on M-algebras.