LAUSR

Finite and infinite dimensional Lie group structures on Riordan groups

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1 Published in 2017 at "Advances in Mathematics"

DOI: 10.1016/j.aim.2017.08.033

Abstract: Abstract We introduce a Frechet Lie group structure on the Riordan group. We give a description of the corresponding Lie algebra as a vector space of infinite lower triangular matrices. We describe a natural linear… read more here.

Keywords: lie group; lie; group; groups finite ... See more keywords

Distinguishing crystallographic groups by their finite quotients

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0 Published in 2021 at "Journal of Algebra"

DOI: 10.1016/j.jalgebra.2020.06.033

Abstract: Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients. read more here.

Keywords: finite quotients; groups finite; distinguishing crystallographic; crystallographic groups ... See more keywords

On the lower central series of the free nilpotent groups of finite rank

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1 Published in 2019 at "Communications in Algebra"

DOI: 10.1080/00927872.2018.1539175

Abstract: Abstract In their article, “On the derived subgroup of the free nilpotent groups of finite rank” R. D. Blyth, P. Moravec, and R. F. Morse describe the structure of the derived subgroup of a free… read more here.

Keywords: group; free nilpotent; groups finite; lower central ... See more keywords

On character formulae for Weil representations for unitary groups over finite fields

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1 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1926472

Abstract: Abstract We calculate characters of Weil representations of unitary groups over finite fields geometrically. As a byproduct, we deduce another proof of Gérardin’s trace formula for the Weil representation. Our main ingredient is an explicit… read more here.

Keywords: weil representations; representations unitary; finite fields; unitary groups ... See more keywords

On rack homology groups of finite quandles via permutations

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1 Published in 2019 at "Journal of Knot Theory and Its Ramifications"

DOI: 10.1142/s0218216519400042

Abstract: A quandle is a set equipped with a binary operation satisfying three quandle axioms. It also can be expressed as a sequence of permutations of the underlying set satisfying certain conditions. In this paper, we… read more here.

Keywords: rack homology; groups finite; quandles via; finite quandles ... See more keywords