Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation
Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation
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Yang-Baxter 方程的集合论类型解的拟双代数
DOI：
10.1007/s11005-022-01572-9
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发表时间：
2022
影响因子：
1.2
通讯作者：
Doikou A
中科院分区：
文献类型：
--
作者：
Doikou A
我们研究了从Yang-Baxter方程的对合非退化集合论解及其q-类似物中出现的量子代数类。在给出了准双代数和可容许的Drinfeld扭转的一些普适结果之后，我们证明了由集合论解及其q-类似物产生的量子代数实际上是准三角准双代数。具体的说明性例子与我们的一般发现相一致。在集论解的q变形情况下，我们也构造了类似于集论解的可容许的Drinfeld扭曲，但受到q变形所规定的某些额外约束。这些发现极大地推广了最近关于集合论解及其q变形类似物的相关结果。
We examine classes of quantum algebras emerging from involutive, non-degenerate set-theoretic solutions of the Yang–Baxter equation and theirq-analogues. After providing some universal results on quasi-bialgebras and admissible Drinfeld twists, we show that the quantum algebras produced from set-theoretic solutions and theirq-analogues are in fact quasi-triangular quasi-bialgebras. Specific illustrative examples compatible with our generic findings are worked out. In theq-deformed case of set-theoretic solutions, we also construct admissible Drinfeld twists similar to the set-theoretic ones, subject to certain extra constraints dictated by theq-deformation. These findings greatly generalize recent relevant results on set-theoretic solutions and theirq-deformed analogues.