Two-dimensional Q-algebras

q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU (N ) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality...

Large N Expansion of q-Deformed Two-Dimensional Yang-Mills Theory and Hecke Algebras

We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality o...

Decomposition of Finite - Dimensional Matrix Algebras over F q

Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field Fq(y), where Fq is the finite field with q elements. A fi...

Varieties of two-dimensional cylindric algebras II

In [2] we investigated the lattice Λ(Df 2) of all subvarieties of the variety Df2 of two-dimensional diagonal free cylindric algebras. In the present paper we investigate the lattice Λ(CA2) of all subvarieties of the variety CA2 of two-dimensional cylindric algebras. We prove that the cardinality of Λ(CA2) is that of the continuum, give a criterion for a subvariety of CA2 to be locally finite, ...

Varieties of Two-dimensional Cylindric Algebras