"클리퍼드 대수"의 두 판 사이의 차이

2011년 10월 2일 (일) 07:13 판

#
quadratic space \((V,Q)\)
Q : non-degenerate quadratic form, defines a symmetric bilinear form \(<x,y>\)
Clifford algebra : associative algebra generated by vectors in V with relations
- \(v^2=Q(v)\)
- \(vw+wv=2<w,v>\)
Clifford algebras may be thought of as quantizations (cf. quantization (physics), Quantum group) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra.

Lachièze-Rey, Marc. 2009. “Spin and Clifford Algebras, an Introduction”. Advances in Applied Clifford Algebras 19 (3-4): 687-720. doi:10.1007/s00006-009-0187-y.
http://www.math.ucla.edu/~vsv/papers/ch5.pdf

@@ 2번째 줄: / 2번째 줄: @@
 * [[#]]
+* quadratic space <math>(V,Q)</math>
+* Q : non-degenerate quadratic form, defines a symmetric bilinear form <math><x,y></math>
+*  Clifford algebra : associative algebra generated by vectors in V with relations<br>
+** <math>v^2=Q(v)</math>
+** <math>vw+wv=2<w,v></math>
-quadratic space <math>(V,Q)</math>
+*  Clifford algebras may be thought of as quantizations (cf. quantization (physics), Quantum group) of the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra.
-Q : non-degenerate quadratic form