Zobrazeno 1 - 10
of 46
pro vyhledávání: '"57M27, 17B37"'
For $G$ a commutative group, we give a purely Hopf $G$-coalgebra construction of $G$-colored $3$-manifolds invariants using the notion of modified integral.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2209.04691
The second author constructed a topological ribbon Hopf algebra from the unrolled quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$. We generalize this fact to the context of unrolled quantum groups and construct the associated
Externí odkaz:
http://arxiv.org/abs/2006.12050
Autor:
Ha, Ngoc Phu
It is known that the category $\mathscr{C}^H$ of nilpotent weight modules over the quantum group associated with the super Lie algebra $\mathfrak{sl}(2|1)$ is a relative pre-modular $G$-category. Its modified trace enables to define an invariant of $
Externí odkaz:
http://arxiv.org/abs/2001.10748
Autor:
Ha, Ngoc Phu
We prove the unrolled superalgebra $\mathcal{U}_{\xi}^{H}\mathfrak{sl}(2|1)$ has a completion which is a ribbon superalgebra in a topological sense where $\xi$ is a root of unity of odd order. Using this ribbon superalgebra we construct its universal
Externí odkaz:
http://arxiv.org/abs/1806.08277
The Hennings invariant for the small quantum group associated to an arbitrary simple Lie algebra at a root of unity is shown to agree with Jones- Witten-Reshetikhin-Turaev invariant arising from Chern-Simons filed theory for the same Lie algebra and
Externí odkaz:
http://arxiv.org/abs/1701.01423
Autor:
Ha, Ngoc Phu
In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. This construction based on nilpotent irreducible finite dimensional representations of quantum group
Externí odkaz:
http://arxiv.org/abs/1607.03728
Autor:
Pavlyuk, Anatoliy M.
Publikováno v:
Algebras, Groups and Geometries Vol.31, No.2 (2014) 175-182
We introduce the deformed fermionic numbers, corresponding to the skein relations, the main characteristics of knots and links. These fermionic numbers allow one to restore the skein relations. For the Alexander (Jones) skein relation we introduce co
Externí odkaz:
http://arxiv.org/abs/1601.03589
Autor:
Pavlyuk, Anatoliy M.
Publikováno v:
Algebras, Groups and Geometries Vol.29, No.2 (2012) 173-180
We propose an algorithm which allows to derive the generalized Alexander polynomial invariants of knots and links with the help of the q,p-numbers, appearing in bosonic two-parameter quantum algebra. These polynomials turn into HOMFLY ones by applyin
Externí odkaz:
http://arxiv.org/abs/1510.06573
Autor:
Habiro, Kazuo, Lê, Thang T. Q.
Publikováno v:
Geom. Topol. 20 (2016) 2687-2835
For each finite dimensional, simple, complex Lie algebra $\mathfrak g$ and each root of unity $\xi$ (with some mild restriction on the order) one can define the Witten-Reshetikhin-Turaev (WRT) quantum invariant $\tau_M^{\mathfrak g}(\xi)\in \mathbb C
Externí odkaz:
http://arxiv.org/abs/1503.03549
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic properties determine topological invariants. We prove that fusion categories of
Externí odkaz:
http://arxiv.org/abs/1312.7188