相关论文: Clifford correspondence for algebras

I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in…

Let A be a commutative ring with 1/2 in A. In this paper, we define new characteristic classes for finitely generated projective A-modules V provided with a non degenerate quadratic form. These classes belong to the usual K-theory of A.…

Given a fixed binary form $f(u,v)$ of degree $d$ over a field $k$, the associated \emph{Clifford algebra} is the $k$-algebra $C_f=k\{u,v\}/I$, where $I$ is the two-sided ideal generated by elements of the form $(\alpha u+\beta…

We introduce a Hopf algebra structure of subword complexes, including both finite and infinite types. We present an explicit cancellation free formula for the antipode using acyclic orientations of certain graphs, and show that this Hopf…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. Let $T$ be a tilting $A$-module and $B={\rm End}_A\ T$ be the endomorphism algebra of $T$. In this paper, we consider the correspondence between the tilting…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

We introduce a method to define $C^*$-algebras from $C^*$-correspondences. Our construction generalizes Cuntz-Pimsner algebras, crossed products by Hilbert $C^*$-modules, and graph algebras.

Let $\Lambda$ be a finite dimensional algebra. In this paper we show that there is a natural bijection between cosilting modules in Mod$\Lambda$ and semibricks in Mod$\Lambda$ satisfying some condition. Also this bijection restricts to a…

I argue that the Hodge structure on a Euclidean Clifford algebra $Cl(n)$ provides a way to generalise K\"ahler structure to higher dimensions, in the sense that the paired variables are now associated with $k-$ and $(n-k)-$ dimensional…

We investigate commutative analogues of Clifford algebras -- algebras whose generators square to $\pm1$ but commute, instead of anti-commuting as they do in Clifford algebras. We observe that commutativity allows for elegant results. We…

Following Herranz and Santander [Herranz F.J., Santander M., Mem. Real Acad. Cienc. Exact. Fis. Natur. Madrid 32 (1998), 59-84, physics/9702030] we will construct homogeneous spaces based on possible kinematical algebras and groups [Bacry…

{\sc CLIFFORD} is a Maple package for computations in Clifford algebras $\cl (B)$ of an arbitrary symbolic or numeric bilinear form B. In particular, B may have a non-trivial antisymmetric part. It is well known that the symmetric part g of…

Let $\FRAK{g}$ be a classical simple Lie superalgebra. To every nilpotent orbit $\cal O$ in $\FRAK{g}_0$ we associate a Clifford algebra over the field of rational functions on $\cal O$. We find the rank, $k(\cal O)$ of the bilinear form…

An algebraic description of basic discrete symmetries (space reversal P, time reversal T and their combination PT) is studied. Discrete subgroups of orthogonal groups of multidimensional spaces over the fields of real and complex numbers…

We give a graphical calculus for a categorification of a Clifford algebra and its Fock space representation via differential graded categories. The categorical action is motivated by the gluing action between the contact categories of…

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using…

All 7-dimensional subalgebras of the 8-dimensional Clifford algebra over the field C of complex numbers are found. Canonical bases are used throughout the determination. It is found that the 8-dimensional Clifford algebra over C has exactly…

The Hopf envelope of a bialgebra is the free Hopf algebra generated by the given bialgebra. Its existence, as well as that of the cofree Hopf algebra, is a well-known fact in Hopf algebra theory, but their construction is not particularly…

We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using…

This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)