✦ LIBER ✦

Idempotent structure of Clifford algebras

✍ Scribed by Pertti Lounesto; G. P. Wene

Publisher: Springer Netherlands
Year: 1987
Tongue: English
Weight: 387 KB
Volume: 9
Category: Article
ISSN: 0167-8019
DOI: 10.1007/bf00047537

No coin nor oath required. For personal study only.

✦ Synopsis

Spinor spaces can be represented as minimal left ideals of Clifford algebras and they are generated by primitive idempotents. Primitive idempotents of the Clifford algebras Rp.q are shown to be products of mutually nonannihilating commuting idempotent factors I(1 +cT), where the k = q -rq_p basis elements eT satisfy e~-= 1. The lattice generated by a set of mutually annihilating primitive idempotents is examined. The final result characterizes all Clifford algebras Rp.u with an anti-involution such that each symmetric element is either a nilpotent or then some right multiple of it is a nonzero symmetric idempotent. This happens when p + q ~< 3 and (p, q) ~ (2, 1).

📜 SIMILAR VOLUMES

Idempotent matrices from a generalized C

Idempotent matrices from a generalized Clifford algebra

✍ Alladi Ramakrishnan; P.S. Chandrasekaran; N.R. Ranganathan; T.S. Santhanam; R. V 📂 Article 📅 1969 🏛 Elsevier Science 🌐 English ⚖ 66 KB

Operator Algebras of Idempotents

✍ Vern I. Paulsen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 167 KB

We introduce the concept of a matricial Schur ideal, which serves as a dual object for operator algebras generated by a finite set of idempotents. Using matricial Schur ideals and some factorization theorems for tensor products of operator algebras, we are able to obtain matrix-valued interpolation

Subalgebra systems of idempotent entropi

Subalgebra systems of idempotent entropic algebras

✍ Anna B Romanowska; Jonathan D.H Smith 📂 Article 📅 1989 🏛 Elsevier Science 🌐 English ⚖ 890 KB

Orthogonal and symplectic clifford algeb

Orthogonal and symplectic clifford algebras (spinor structures)

✍ S. E. Payne 📂 Article 📅 1991 🏛 Springer Netherlands 🌐 English ⚖ 171 KB

Spinors were first used under that name by physicists in the field of quantum mechanics. E. Cartan (see [1]) discovered a more geometrical setting for them, at least in the case that the scalar field was either the reals or the complexes. In 1954, C. Chevalley [2] gave the definitive treatment for t

A generalisation of Clifford algebras

✍ M. A. Knus 📂 Article 📅 1969 🏛 Springer-Verlag 🌐 French ⚖ 313 KB

Clifford algebras obtained by twisting o

Clifford algebras obtained by twisting of group algebras

✍ Helena Albuquerque; Shahn Majid 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 144 KB

We investigate the construction and properties of Cli ord algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z n 2 by a cocycle. Our approach is more general than the usual one based on generators and relations. We obtain, in particu