Roots of unity as a Lie algebra

A. Davydov; R. Street

Roots of unity as a Lie algebra

Research output: Contribution to journal › Article › peer-review

Abstract

This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the "substitude" structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.

Original language	English
Pages (from-to)	683-690
Number of pages	8
Journal	Georgian Mathematical Journal
Volume	9
Issue number	4
Publication status	Published - 2002

Keywords

Lie algebra
operad
substitude
species
cyclic group

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title = "Roots of unity as a Lie algebra",

abstract = "This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the {"}substitude{"} structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.",

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T1 - Roots of unity as a Lie algebra

AU - Davydov, A.

AU - Street, R.

PY - 2002

Y1 - 2002

N2 - This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the "substitude" structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.

AB - This note gives a categorical development arising from a theorem of A. A. Klyachko relating the Lie operad to roots of unity. We examine the "substitude" structure on the groupoid C whose homsets are the cyclic groups. The roots of unity representations of the cyclic groups form a Lie algebra for a certain oplax monoidal structure on the category of linear representations of C.

KW - Lie algebra

KW - operad

KW - substitude

KW - species

KW - cyclic group

M3 - Article

VL - 9

SP - 683

EP - 690

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

SN - 1572-9176

IS - 4

ER -