Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Ng, Siu-Hung"'
Given a premodular category $\mathcal{C}$, we show that its $R$-symbol can be recovered from its $T$-matrice, fusion coefficients and some 2nd generalized Frobenius-Schur indicators. In particular, if $\mathcal{C}$ is modular, its $R$-symbols for a c
Externí odkaz:
http://arxiv.org/abs/2408.02748
Autor:
Ng, Siu-Hung, Wang, Xingting
Let $\Bbbk$ be an algebraically closed field of characteristic $p>0$. We study the general structures of $p^n$-dimensional Hopf algebras over $\Bbbk$ with $p^{n-1}$ group-like elements or a primitive element generating a $p^{n-1}$-dimensional Hopf su
Externí odkaz:
http://arxiv.org/abs/2308.10471
We use the computer algebraic system GAP to classify modular data up to rank 11, and integral modular data up to rank 12. This extends the previously obtained classification of modular data up to rank 6. Our classification includes all the modular da
Externí odkaz:
http://arxiv.org/abs/2308.09670
Publikováno v:
Proceedings of the American Mathematical Society, Volume 151, Number 4, April 2023, Pages 1415--1431
We introduce the notions of symmetric and symmetrizable representations of $\text{SL}_2(\mathbb{Z})$. The linear representations of $\text{SL}_2(\mathbb{Z})$ arising from modular tensor categories are symmetric and have congruence kernel. Conversely,
Externí odkaz:
http://arxiv.org/abs/2203.15701
Publikováno v:
Communications in Mathematical Physics (2023)
Modular data is the most significant invariant of a modular tensor category. We pursue an approach to the classification of modular data of modular tensor categories by building the modular $S$ and $T$ matrices directly from irreducible representatio
Externí odkaz:
http://arxiv.org/abs/2203.14829
Autor:
Mason, Geoffrey, Ng, Siu-Hung
Publikováno v:
J. Pure Appl. Algebra, vol. 227 (2023) no. 5, Paper No. 107264, 26
In a previous paper the authors constructed a class of quasi-Hopf algebras $D^{\omega}(G, A)$ associated to a finite group $G$, generalizing the twisted quantum double construction. We gave necessary and sufficient conditions, cohomological in nature
Externí odkaz:
http://arxiv.org/abs/2203.05500
Let $V$ be a simple, rational, $C_2$-cofinite vertex operator algebra and $G$ a finite group acting faithfully on $V$ as automorphisms, which is simply called a rational vertex operator algebra with a $G$-action. It is shown that the category ${\cal
Externí odkaz:
http://arxiv.org/abs/2108.05225
Publikováno v:
Comm. Math. Phys. 390, 1271-1310 (2022)
In this paper, we study modular categories whose Galois group actions on their simple objects are transitive. We show that such modular categories admit unique factorization into prime transitive factors. The representations of $SL_2(\mathbb{Z})$ ass
Externí odkaz:
http://arxiv.org/abs/2007.01366
Publikováno v:
Advances in Mathematics Volume 404, Part A, 6 August 2022, 108388
In this paper, we introduce the definitions of signatures of braided fusion categories, which are proved to be invariants of their Witt equivalence classes. These signature assignments define group homomorphisms on the Witt group. The higher central
Externí odkaz:
http://arxiv.org/abs/2002.03570
Let $V$ be a vertex operator superalgebra with the natural order 2 automorphism $\sigma$. Under suitable conditions on $V$, the $\sigma$-fixed subspace $V_{\bar 0}$ is a vertex operator algebra and the category $C_{V_{\bar 0}}$ of $V_{\bar 0}$-module
Externí odkaz:
http://arxiv.org/abs/2001.00365