Videolibrary Video Library Archive Most viewed videos Search RSS New in collection

Adian 90: Conference on Mathematical Logic, Algebra, and Computation
July 5, 2021 13:30–14:15, Moscow, Steklov Mathematical Institute of RAS (Moscow) and online in Zoom  Identities in twisted Brauer monoids

M. V. Volkov

Ural Federal University, Ekaterinburg
 Video records: MP4 1,043.5 Mb  Видео не загружается в Ваш браузер: Активируйте JavaScript в Вашем браузере Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080 Сообщите администратору портала о данной ошибке

Abstract: The twisted Brauer monoid $\mathcal{W}_n$ is the monoid generated by $s_1,…,s_{n-1},h_1,…,h_{n-1},c$, subject to the following relations that hold for all $i,j=1,…,n-1$:
\begin{align*} &h_{i}h_{j}=h_{j}h_{i}, s_{i}s_{j}=s_{j}s_{i}, h_{i}s_{j}=s_{j}h_{i} &&if |i-j|\ge 2;&h_{i}h_{j}h_{i}=h_{i}, s_{i}s_{j}s_{i}=s_{j}s_{i}s_{j}, s_is_jh_i = h_js_is_j &&if |i-j|=1;&h_{i}^2=ch_{i}=h_{i}c, s_{i}^2=1, cs_{i}=s_{i}c, s_ih_i = h_is_i=h_i. && \end{align*}
The submonoid $\mathcal{K}_n$ of $\mathcal{W}_n$ generated by $h_1,…,h_{n-1},c$ is called the Kauffman monoid. Identities in Kauffman monoids were studied in [1,2]. It has been shown that the identity checking problem for the monoids $\mathcal{K}_3$ and $\mathcal{K}_4$ is decidable in polynomial time.
Theorem. The identity checking problem for the monoid $\mathcal{W}_n$ with $n\ge4$ is coNP-complete.
The complexity of identity checking problem for the monoid $\mathcal{W}_3$ still remains unknown.

Language: English

References
1. Chen Yuzhu, Hu Xun, Kitov N. V., Luo Yanfeng, Volkov M. V., “Identities of the Kauffman monoid $\mathcal{K}_3$”, Comm. Algebra, 48:5 (2020), 1956–1968
2. Kitov N. V., Volkov M. V., “Identities of the Kauffman monoid $\mathcal{K}_4$ and of the Jones monoid $\mathcal{J}_4$”, Fields of Logic and Computation III, Lect. Notes Comp. Sci., 12180, Springer, Cham, 2020, 156–178

 SHARE:       Contact us: math-net2022_01 [at] mi-ras ru Terms of Use Registration to the website Logotypes © Steklov Mathematical Institute RAS, 2022