arXiv subjects

M. K. Pawelkiewicz

Publications and source records attributed to M. K. Pawelkiewicz.

2 recordsLinked to original sources

arXiv2026

Heisenberg and Drinfeld doubles of Uq(gl(1|1)) and Uq(osp(1|2)) super-algebras

We study the Heisenberg double and the Drinfeld double of the Borel half of $Uq (gl(1|1))$ and of the $Uq (gl(1|1))$ when q is a root of unity. We also study the Borel half of Uq (osp(1|2)) for both cases when qis a root of unity and when it is not. We prove the isomorphism between the Heisenberg doubles and the handle algebras, which is missing in the literature, and extend the isomorphism to the graded Heisenberg doubles and the handle algebras in the context of the Z2-graded generalisation of Alekseev-Schomerus combinatorial quantisation of Chern-Simons theory [1, 2], as well as illustrate it on the example of the Heisenberg double of the $Uq (gl(1|1))$ Hopf algebra for q being a root of unity. In addition, we generalise an isomorphism between the Drinfeld double and the loop algebra from the Alekseev-Schomerus combinatorial quantisation to the graded setting.

math.QA↗

arXiv2020

Towards Super Teichmüller Spin TQFT

The quantization of the Teichmüller theory has led to the formulation of the so-called Teichmüller TQFT for 3-manifolds. In this paper we initiate the study of "supersymmetrization" of the Teichmüller TQFT, which we call the super Teichmüller spin TQFT. We obtain concrete expressions for the partition functions of the super Teichmüller spin TQFT for a class of spin 3-manifold geometries, by taking advantage of the recent results on the quantization of the super Teichmüller theory. We then compute the perturbative expansions of the partition functions, to obtain perturbative invariants of spin 3-manifolds. We also comment on the relations of the super Teichmüller spin TQFT to 3-dimensional Chern-Simons theories with complex gauge groups, and to a class of 3d N=2 theories arising from the compactifications of the M5-branes.

hep-th↗