The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions

被引：0
作者：
Johnson-Freyd, Theo [1 ]
机构：
[1] Perimeter Inst Theoret Phys, Waterloo, ON, Canada
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2016年 / 12卷
基金：
美国国家科学基金会;
关键词：
Clifford algebras; quaternions; Bott periodicity; Morita equivalence; quantum Hamiltonian reduction; super symplectic geometry;
D O I：
10.3842/SIGMA.2016.116
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the Morita equivalences Cliff(4) similar or equal to H,Cliff(7) similar or equal to Cliff(-1), and Cliff(8) similar or equal to R arise from quantizing the Hamiltonian reductions R-0 vertical bar 4 //Spin(3), R-0 vertical bar 7 //G(2), and R-0 vertical bar 8 //Spin(7), respectively.
引用
收藏
页数：6
相关论文
共 9 条
[1]  
[Anonymous], 1974, Reports on Mathematical Physics, V5, P121, DOI 10.1016/0034-4877(74)90021-4
[2]  
Arenas R., 2005, THESIS
[3]  
Bryant R. L., 2006, P GOK GEOM TOP C 200
[4]   A Supergeometric Approach to Poisson Reduction [J].
Cattaneo, A. S. ;
Zambon, M. .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 318 (03) :675-716
[5]  
Deligne P., 1996, QUANTUM FIELDS STRIN, V1, P41
[6]  
Deligne P., 1999, Quantum Fields and Strings: A Course for Mathematicians, V1, P41
[7]   CALIBRATED GEOMETRIES [J].
HARVEY, R ;
LAWSON, HB .
ACTA MATHEMATICA, 1982, 148 :47-157
[8]   On homotopy Poisson actions and reduction of symplectic Q-manifolds [J].
Mehta, Rajan Amit .
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2011, 29 (03) :319-328
[9]  
[No title captured]
1