IntroductionThe classical theory of algebraic geometry connects geometric concepts with corresponding notions in commutative algebra. In the recent decades there was an interest in building a parallel theory based on associative (non-commutative) algebras. We will discuss the basic ideas of this developing theory mostly following Ginzburg's lectures as well as several more recent papers.The cla...
AbstractWe introduce certain class of quadratic algebras together with commutative subalgebras generated by additive and multiplicative Dunkl elements correspondingly. We identify these subalgebras with cohomology and K-theories of type A flag varieties. We show that value of Schubert polynomials on additive Dunkl elements is a generating function for the corresponding Littlewood-Richardson coe...