Zobrazeno 1 - 10
of 108
pro vyhledávání: '"Lê, Thang T. Q."'
Autor:
Lê, Thang T. Q., Yu, Tao
We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\mathfrak{S}$ equipped with an ideal triangulatio
Externí odkaz:
http://arxiv.org/abs/2303.08082
Autor:
Costantino, Francesco, Le, Thang T. Q.
We study the behaviour of the Kauffman bracket skein modules of 3-manifolds under gluing along surfaces. For this purpose we extend the notion of Kauffman bracket skein modules to $3$-manifolds with marking consisting of open intervals and circles in
Externí odkaz:
http://arxiv.org/abs/2206.10906
Autor:
Lê, Thang T. Q., Sikora, Adam S.
We develop a theory of stated SL(n)-skein modules, $S_n(M,N),$ of 3-manifolds $M$ marked with intervals $N$ in their boundaries. They consist of linear combinations of $n$-webs with ends in $N$, considered up to skein relations inspired by the relati
Externí odkaz:
http://arxiv.org/abs/2201.00045
We prove that large classes of algebras in the framework of root of unity quantum cluster algebras have the structures of maximal orders in central simple algebras and Cayley-Hamilton algebras in the sense of Procesi. We show that every root of unity
Externí odkaz:
http://arxiv.org/abs/2107.11926
Autor:
Le, Thang T. Q.
We show that the action of the Kauffman bracket skein algebra of a surface $\Sigma$ on the skein module of the handlebody bounded by $\Sigma$ is faithful if and only if the quantum parameter is not a root of 1.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2103.11532
Autor:
Lê, Thang T. Q., Yu, Tao
The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum special linear
Externí odkaz:
http://arxiv.org/abs/2012.15272
Autor:
Bloomquist, Wade, Lê, Thang T. Q.
We study the stated skein modules of marked 3-manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein modules of 3-manifolds. We show that there exists a Chebyshev-Frobeni
Externí odkaz:
http://arxiv.org/abs/2011.02130
Autor:
Lê, Thang T. Q., Yu, Tao
We give a survey of some old and new results about the stated skein modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we discuss the splitting homomorphism for the 3-manifold case, general structures of the stated skein algebra
Externí odkaz:
http://arxiv.org/abs/2005.14577
We show that the if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequenc
Externí odkaz:
http://arxiv.org/abs/1908.05775
Autor:
Costantino, Francesco, Le, Thang T. Q.
We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ providing a topological
Externí odkaz:
http://arxiv.org/abs/1907.11400