Paragrassmann differential calculus

Филиппов, А. Т.; Исаев, А. П.; Kurdikov, A. B.

doi:10.1007/bf01019327

Cited by 27 publications

(50 citation statements)

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“…A complete list of these realizations (versions) and a fairly general approach to constructing algebras Π p+1 (N) have been presented in Ref. [13]. Here we reproduce the results of this work that are essential for understanding the main body of the present paper.…”

Section: Paragrassmann Algebra π P+1supporting

confidence: 74%

“…As it was already mentioned, in the non-degenerate case the numbers b i are completely determined by the numbers α k , so we can use the symbol {α} as well as {b}. An interesting fact is that nontrivial algebras (α 1 = 0) may be degenerate if and only if p + 1 is a composite number [13]. We will see later that the arithmetic properties of p + 1 are also important in constructing paraconformal transformations.…”

Section: Paragrassmann Algebra π P+1mentioning

confidence: 99%

“…As we shall see in Sect.3, this is not the case for their paraanalogs CON p and Con p since the paragrassmann algebra of 'other thetas' is a much more complicated object than the Grassmann one (and, probably, not uniquely defined, see [13]). In particular, we do not know at the moment simple and general commutation rules between the elements of the paragrassmann algebra.…”

Section: Introductionmentioning

confidence: 99%

“…However, in some calculations the existence of the exact matrix representation (2.11), (2.12) is very useful for deriving version-covariant identities in the algebra Π p+1 . For instance, using the representation it is easy to check that 13) and to find many other relations. Here we have introduced the notation…”

Section: Paragrassmann Algebra π P+1mentioning

confidence: 99%

“…A detailed description of the differential calculus with one and many variables is given in Ref. [13]. In Sect.3, we first discuss main properties of the fractional derivative D (D p+1 = ∂ z ) which are valid in any version of the paragrassmann calculus.…”

Section: Introductionmentioning

confidence: 99%

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Para-Grassmann Extensions of the Virasoro Algebra

Филиппов

Исаев

Kurdikov

1993

Int. J. Mod. Phys. A

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The paragrassmann differential calculus is briefly reviewed. Algebras of the transformations of the para-superplane preserving the form of the parasuperderivative are constructed and their geometric meaning is discussed. A new feature of these algebras is that they contain generators of the automorphisms of the paragrassmann algebra (in addition to Ramond-Neveu-Schwarz -like conformal generators). As a first step in analyzing these algebras we introduce more tractable multilinear algebras not including the new generators. In these algebras there exists a set of multilinear identities based on the cyclic polycommutators. Different possibilities of the closure are therefore admissible. The central extensions of the algebras are given. Their number varies from 1 to [ p+1 2 ] depending on the form of the closure chosen. Finally, simple explicit examples of the paraconformal transformations are given.

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Section: Paragrassmann Algebra π P+1supporting

confidence: 74%

Section: Paragrassmann Algebra π P+1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Paragrassmann Algebra π P+1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations