Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-12-10
Physics
High Energy Physics
High Energy Physics - Theory
12 pages
Scientific paper
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 $p = 4, N = 4$.
Filippov Alexandre T.
Kurdikov A. B.
No associations
LandOfFree
Paragrassmann Algebras with Many Variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Paragrassmann Algebras with Many Variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Paragrassmann Algebras with Many Variables will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171780