Quantum groups and generalized circular elements

NEW METHODS FOR CONSTRUCTING GENERALIZED GROUPS, TOPOLOGICAL GENERALIZED GROUPS, AND TOP SPACES

‎‎The purpose of this paper is to introduce new methods for constructing generalized groups, generalized topological groups and top spaces. We study some properties of these structures and present some relative concrete examples. Moreover, we obtain generalized groups by using of Hilbert spaces and tangent spaces of Lie groups, separately.

Group-like Elements in Quantum Groups and Feigin’s Conjecture

Let A be an arbitrary symmetrizable Cartan matrix of rank r, and n = n+ be the standard maximal nilpotent subalgebra in the Kac-Moody algebra associated with A (thus, n is generated by E1, . . . , Er subject to the Serre relations). Let Ûq(n) be the completion (with respect to the natural grading) of the quantized enveloping algebra of n. For a sequence i = (i1, . . . , im) with 1 ≤ ik ≤ r, let...

PRECOMPACT TOPOLOGICAL GENERALIZED GROUPS

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

Generalized Covering Groups and Direct Limits

Transposable elements and circular DNAs

Circular DNAs are extra-chromosomal fragments that become circularized by genomic recombination events. We have recently shown that yeast LTR elements generate circular DNAs through recombination events between their flanking long terminal repeats (LTRs). Similarly, circular DNAs can be generated by recombination between LTRs residing at different genomic loci, in which case the circular DNA wi...