A Combinatorial Approach to Involution and delta-Regularity I: Involutive Bases in Polynomial Algebras of Solvable Type

PROPs for involutive monoids and involutive bimonoids

The category of involutive non-commutative sets encodes the structure of an involution compatible with a (co)associative (co)multiplication. We prove that the category of involutive bimonoids in a symmetric monoidal category is equivalent to the category of algebras over a PROP constructed from the category of involutive non-commutative sets.

对合Brauer群与Poincaré环

Involutive Brauer groups and Poincaré rings

利用Poincaré ∞-范畴形式化定义并研究带有λ-厄米配对的线丛模叠和带有对合的Azumaya代数的Morita等价类模叠，引入Poincaré Picard群和Poincaré Brauer群，并证明它们与Parimala-Srinivas的对合Brauer群的关系及差异。

Involutive Bases Algorithm Incorporating F5 Criterion

Faugere's F5 algorithm is the fastest known algorithm to compute Groebner bases. It has a signature-based and an incremental structure that allow to apply the F5 criterion for deletion of unnecessary reductions. In this paper, we present an involutive completion algorithm which outputs a minimal involutive basis. Our completion algorithm has a nonincremental structure and in addition to the involutive form of Buchberger's criteria it applies the F5 criterion whenever this criterion is applicable in the course of completion to involution. In doing so, we use the G2V form of the F5 criterion dev…