superalgebra and (synthetic ) supergeometry
The concept of a division superalgebra (also super division algebra) is the analog of that of division algebras in the context of superalgebra. As such, a division superalgebra is a superalgebra in which every nonzero homogeneous element is invertible.
The classification of the associative real division superalgebras by a “ten-fold way” is essentially attributed to Dyson (1962) by Freed & Moore (2013, Appendix C) (in the context of the K-theory classification of topological phases of matter), further expanded on in Moore (2013), Section 14 and Geiko & Moore (2021).
Freeman Dyson, The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics, J. Math. Phys. 3 1199 (1962) [doi:10.1063/1.1703863]
Todd Trimble, The super Brauer group and super division algebras (April 27, 2005) [webpage]
Daniel Freed, Gregory Moore, Appendix C of: Twisted equivariant matter, Ann. Henri Poincaré 14 (2013) 1927-2023 [arXiv:1208.5055, doi:10.1007/s00023-013-0236-x]
Gregory Moore, Section 14 of: Quantum symmetries and compatible Hamiltonians (2013) [pdf]
Roman Geiko, Gregory W. Moore, Dyson’s classification and real division superalgebras, April 2021, Journal of High Energy Physics 2021(4):299, (doi: 10.1007/jhep04(2021)299).
Last revised on April 6, 2023 at 13:13:20. See the history of this page for a list of all contributions to it.