منابع مشابه
Clifford Algebras and Their Representations
Introductory and historical remarks Clifford (1878) introduced his ‘geometric algebras’ as a generalization of Grassmann algebras, complex numbers and quaternions. Lipschitz (1886) was the first to define groups constructed from ‘Clifford numbers’ and use them to represent rotations in a Euclidean space. É. Cartan discovered representations of the Lie algebras son(C) and son(R), n > 2, that do ...
متن کاملClifford Theory for Cocentral Extensions
The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.
متن کاملClifford representations in integrable systems
In this paper we analyze integrable systems from a Clifford algebra point of view. This approach allows us to give a clear representation theoretic exposition of techniques used in spin systems, thereby showing their naturality. We then extend this approach to the analysis of the XX-model with nondiagonal boundaries which is among others related to growing and fluctuating interfaces and stochas...
متن کاملClifford Theory for Association Schemes
Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset coniatns conjugate characters with same multiplicities. Moreover some strong relations are obtained.
متن کاملClifford theory for tensor categories
A graded tensor category over a group G will be called a strongly G-graded tensor category if every homogeneous component has at least one invertible object. Our main result is a description of the module categories over a strongly G-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of G.
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2016
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-016-9628-1