Paragrassmann Algebras with Many Variables
| dc.creator | Filippov, A. T. | |
| dc.creator | Kurdikov, A. B. | |
| dc.date | 1993-12-10 | |
| dc.date.accessioned | 2026-07-07T04:19:54Z | |
| dc.date.available | 2026-07-07T04:19:54Z | |
| dc.description | This is a brief review of our recent work attempted at a generalization of the Grassmann algebra to the paragrassmann ones. The main aim is constructing an algebraic basis for representing `fractional' symmetries appearing in $2D$ integrable models and also introduced earlier as a natural generalization of supersymmetries. We have shown that these algebras are naturally related to quantum groups with $q = {\rm root \;of \; unity}$. By now we have a general construction of the paragrassmann calculus with one variable and preliminary results on deriving a natural generalization of the Neveu--Schwarz--Ramond algebra. The main emphasis of this report is on a new general construction of paragrassmann algebras with any number of variables, N. It is shown that for the nilpotency indices $(p + 1) = 3, 4, 6$ the algebras are almost as simple as the Grassmann algebra (for which $(p + 1) = 2$). A general algorithm for deriving algebras with arbitrary p and N is also given. However, it is shown that this algorithm does not exhaust all possible algebras, and the simplest example of an `exceptional' algebra is presented for $p = 4, N = 4$. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9312081 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9312081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/53757 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Paragrassmann Algebras with Many Variables | |
| dc.type | text |