A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

I summarize some recent results obtained in collaboration with P. Bouwknegt and K. Pilch on the spectrum of physical states in W 3 gravity coupled to c = 2 matter. In particular, it is shown that the algebra of operators corresponding to physical states – defined as a semi-infinite (or BRST) cohomology of the W 3 algebra – carries the structure of a G-algebra. This G-algebra has a quotient whic...

The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...

In intensional type theory, it is not always possible to form the quotient of a type by an equivalence relation. However, quotients are extremely useful when formalizing mathematics, especially in algebra. We provide a Coq library with a pragmatic approach in two complementary components. First, we provide a framework to work with quotient types in an axiomatic manner. Second, we program constr...

We realize the current algebra of a Kac-Moody algebra as a quotient of a semi-direct product of the Kac-Moody Lie algebra and the free Lie algebra of the Kac-Moody algebra. We use this realization to study the representations of the current algebra. In particular we see that every ad-invariant ideal in the symmetric algebra of the Kac-Moody algebra gives rise in a canonical way to a representat...

In this paper we study the vertex operator algebra Dch(H,Γ) constructed from fixed points of chiral differential operators on upper half plane which is holomorphic at all cusps, under action a congruence subgroup Γ. To end, introduce an SL(2,R)-invariant filtration labeled by partition pairs and its successive quotient. We show that quotient cuspidal condition isomorphic to space modular forms....

Let A be a Koszul Artin-Schelter regular algebra, σ graded automorphism of and δ degree-one -derivation . We introduce an invariant for called the -divergence describe Nakayama Ore extension B = [ z ; , ] explicitly using construct twisted superpotential ω ˆ so that it is derivation quotient algebra defined by also determine all extensions noetherian algebras dimension 2 compute their automorph...

In this paper, by considering the notion of hyper hoop-algebras, we define the concepts of (strong) regular relations on hyper hoop-algebras and investigate some properties of them. Then we construct a quotient (hyper) hoop-algebra by a (strong)regular relation on hyper hoop-algebras. Finally, we define the notion of maximal filter and we investigate the relation between quotient simple hyper h...

We study a class of representations over the degenerate double affine Hecke algebra of gln by an algebraic method. As fundamental objects in this class, we introduce certain induced modules and study some of their properties. In particular, it is shown that these induced modules have unique simple quotient modules under certain conditions. Moreover, we show that any simple module in this class ...

A notion of meromorphic open-string vertex algebra is introduced. A meromorphic open-string vertex algebra is an open-string vertex algebra in the sense of Kong and the author satisfying additional rationality (or meromorphicity) conditions for vertex operators. The vertex operator map for a meromorphic open-string vertex algebra satisfies rationality and associativity but in general does not s...