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Problems in the theory of quantum groups

Shuzhou Wang (1997)

Banach Center Publications

This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.

Productivity of the Zariski topology on groups

Dikran N. Dikranjan, D. Toller (2013)

Commentationes Mathematicae Universitatis Carolinae

This paper investigates the productivity of the Zariski topology ℨ G of a group G . If 𝒢 = { G i ∣ i ∈ I } is a family of groups, and G = ∏ i ∈ I G i is their direct product, we prove that ℨ G ⊆ ∏ i ∈ I ℨ G i . This inclusion can be proper in general, and we describe the doubletons 𝒢 = { G 1 , G 2 } of abelian groups, for which the converse inclusion holds as well, i.e., ℨ G = ℨ G 1 × ℨ G 2 . If e 2 ∈ G 2 is the identity element of a group G 2 , we also describe the class Δ of groups G 2 such that G 1 × { e 2 } is an elementary algebraic subset of G 1 × G 2 for every group G 1 . We show among others, that Δ is stable...

Currently displaying 81 – 100 of 140