ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Doi, Shunya, Aizawa, Naruhiko
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211352
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics. Shunya Doi and Naruhiko Aizawa. SIGMA 17 (2021), 071, 14 pages

Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models...