Chekhov-Mazzocco-braid18.pdf (283.23 kB)
Download file

Poisson algebras of block-upper-triangular bilinear forms and braid group action

Download (283.23 kB)
journal contribution
posted on 27.06.2013, 08:27 authored by Leonid Chekhov, Marta Mazzocco
In this paper we study a quadratic Poisson algebra structure on the space of bilinear forms on CN with the property that for any n,m 2 N such that nm = N, the restriction of the Poisson algebra to the space of bilinear forms with block-upper-triangular matrix composed from blocks of size m × m is Poisson. We classify all central elements and characterise the Lie algebroid structure compatible with the Poisson algebra. We integrate this algebroid obtaining the corresponding groupoid of morphisms of block-uppertriangular bilinear forms. The groupoid elements automatically preserve the Poisson algebra. We then obtain the braid group action on the Poisson algebra as elementary generators within the groupoid. We discuss the affinisation and quantisation of this Poisson algebra, showing that in the case m = 1 the quantum affine algebra is the twisted q-Yangian for on and for m = 2 is the twisted q-Yangian for sp2n. We describe the quantum braid group action in these two examples and conjecture the form of this action for any m > 2. Finally, we give an R-matrix interpretation of our results and discuss the relation with Poisson–Lie groups.

History

School

  • Science

Department

  • Mathematical Sciences

Citation

CHEKHOV, L. and MAZZOCCO, M., (2013). Poisson algebras of block-upper-triangular bilinear forms and braid group action. Communications in Mathematical Physics, 322 (1) , pp. 49-71.

Publisher

© Springer Verlag

Version

AM (Accepted Manuscript)

Publication date

2010

Notes

This article was published in the journal, Communications in Mathematical Physics [© Springer Verlag] and the definitive version is available at: http://link.springer.com/article/10.1007/s00220-013-1757-3.

Language

en

Usage metrics

Keywords

Exports