Clifford A-algebras of Quadratic A-Modules

被引：0

作者：

Ntumba, Patrice P. ^{[1
]}

机构：

[1] Univ Pretoria, Dept Math & Appl Math, ZA-0002 Hatfield, South Africa

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2012年 / 22卷 / 04期

关键词：

Clifford A-morphism; quadratic A-module; Riemannian quadratic A-module; Clifford A-algebra; principal A-automorphism; even sub-A-algebra; A-antiautomorphism; sub-A-module of odd products;

D O I：

10.1007/s00006-012-0333-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Clifford A-algebra of a quadratic A-module (epsilon, q) is an associative and unital A-algebra (i.e. sheaf of A-algebras) associated with the quadratic ShSet(X)-morphism q, and satisfying a certain universal property. By introducing sheaves of sets of orthogonal bases (or simply sheaves of orthogonal bases), we show that with every Riemannian quadratic free A-module of finite rank, say, n, one can associate a Clifford free A-algebra of rank 2(n) . This "main" result is stated in Theorem 3.2.

引用

页码：1093 / 1107

页数：15

共 10 条

[1] [Anonymous], 1981, FORMES QUADRATIQUES
[2] [Anonymous], 2002, ALGEBRA
[3] Chevalley C, 1997, The Algebraic Theory of Spinors and Clifford Algebras
[4] Mallios A., 1998, Geometry of Vector Sheaves: An Axiomatic Approach to Differential Geometry, Vol II: Geometry Examples and Applications, VII
[5] Mallios A., 1998, MATH JAPONICA PLAZA, V48
[6] Mallios A, 2008, INT J THEOR PHYS, V47, P1929, DOI 10.1007/s10773-007-9637-2
[7] Mallios A, 2006, NOTE MAT, V25, P57
[8] Mallios A, 2009, REND CIRC MAT PALERM, V58, P169, DOI 10.1007/s12215-009-0015-1
[9] Ntumba P.P., CZECHOSLOVA IN PRESS
[10] [No title captured]

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