409,757 research outputs found
The Schur-Clifford subgroup of the Brauer-Clifford group
We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group,
similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup
contains exactly the equivalence classes coming from the intended application
to Clifford theory of finite groups. We show that the Schur-Clifford subgroup
is indeed a subgroup of the Brauer-Clifford group, as are certain naturally
defined subsets. We also show that this Schur-Clifford subgroup behaves well
with respect to restriction and corestriction maps between Brauer-Clifford
groups.Comment: Corrected a few typos. Final versio
Hermite and Gegenbauer polynomials in superspace using Clifford analysis
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard
Clifford analysis are generalized to the new framework of Clifford analysis in
superspace in a merely symbolic way. This means that one does not a priori need
an integration theory in superspace. Furthermore a lot of basic properties,
such as orthogonality relations, differential equations and recursion formulae
are proven. Finally, an interesting physical application of the super
Clifford-Hermite polynomials is discussed, thus giving an interpretation to the
super-dimension.Comment: 18 pages, accepted for publication in J. Phys.
Idempotents of Clifford Algebras
A classification of idempotents in Clifford algebras C(p,q) is presented. It
is shown that using isomorphisms between Clifford algebras C(p,q) and
appropriate matrix rings, it is possible to classify idempotents in any
Clifford algebra into continuous families. These families include primitive
idempotents used to generate minimal one sided ideals in Clifford algebras.
Some low dimensional examples are discussed
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