Universal Extension Classes for GL 2

Universal Central Extension of Current Superalgebras

Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras  are very impo...

Lambert series and conjugacy classes in GL

Universal cycles for permutation classes

We define a universal cycle for a class of n-permutations as a cyclic word in which each element of the class occurs exactly once as an n-factor. We give a general result for cyclically closed classes, and then survey the situation when the class is defined as the avoidance class of a set of permutations of length 3, or of a set of permutations of mixed lengths 3 and 4. Résumé. Nous définissons...

Universal Classes for Algebraic Groups

We exhibit cocycles representing certain classes in the cohomology of the algebraic group GLn with coefficients in the representation Γ(gl n ). These classes’ existence was anticipated by van der Kallen, and they intervene in the proof that reductive linear algebraic groups have finitely generated cohomology algebras [18]. Let k be a field of positive characteristic, let A be a finitely generat...

Universal T - matrix for Twisted Quantum gl ( N )

The Universal T-matrix is the capstone of the structure that consists of a quantum group and its dual, and the central object from which spring the T-matrices (monodromies) of all the associated integrable models. A closed expression is obtained for the case of multiparameter (twisted) quantum gℓ(N). The factorized nature of standard quantum groups, that allows the explicit expression for UT to...