1-Cocycles on the group of contactomorphisms on the supercircle S1|3 generalizing the Schwarzian derivative

Title:

1-Cocycles on the group of contactomorphisms on the supercircle S1|3 generalizing the Schwarzian derivative

Creator:

Agrebaoui, Boujemaa and Hattab, Raja

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:09655e67-1105-4962-91c0-1ad625daded1
uuid:09655e67-1105-4962-91c0-1ad625daded1
issn:0011-4642

Subject:

matematika, vektorová pole, derivace funkce, mathematics, vector fields, derivatives (mathematics), contact vector field, cohomology of groups, group of contactomorphisms, super-Schwarzian derivative, invariant differential operator, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

The relative cohomology Hdiff1(K(1|3), osp(2, 3);Dγ,µ(S1|3)) of the contact Lie superalgebra K(1|3) with coefficients in the space of differential operators Dγ,µ(S1|3) acting on tensor densities on S1|3, is calculated in N.Ben Fraj, I. Laraied, S. Omri (2013) and the generating 1-cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative 1-cocycle s(Xf) = D1D2D3(f)α31/2, Xf \in K(1|3) which is invariant with respect to the conformal subsuperalgebra osp(2, 3) of K(1|3). In this work we study the supergroup case. We give an explicit construction of 1-cocycles of the group of contactomorphisms K(1|3) on the supercircle S1|3 generating the relative cohomology Hdiff1(K(1|3), PC(2, 3); Dγ,µ(S1|3) with coefficients in Dγ,µ(S1|3). We show that they possess properties similar to those of the super-Schwarzian derivative 1-cocycle S3(Φ) = EΦ-1 (D1(D2),D3)α31/2, Φ ∈ K(1|3) introduced by Radul which is invariant with respect to the conformal group PC(2, 3) of K(1|3). These cocycles are expressed in terms of S3(Φ) and possess its properties., Boujemaa Agrebaoui, Raja Hattab., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1143-1163

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:4

Harvested from:

CDK

Metadata only:

false