Algebraic inverses on lie algebra comultiplications

Dae Woong Lee

doi:10.3390/SYM12040565

Algebraic inverses on lie algebra comultiplications

Dae Woong Lee^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

2 Scopus citations

Abstract

In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if l(1)_c and r(1)_c are the left and right inverses of the identity 1: L → L on a free graded Lie algebra L, respectively, based on the Lie algebra comultiplication ψ_c: L → L L, then we have l(1) = l(1)_c and r(1) = r(1)_c, where c: L → L L is a commutator.

Original language	English
Article number	565
Journal	Symmetry
Volume	12
Issue number	4
DOIs	https://doi.org/10.3390/SYM12040565
State	Published - 2020.04.1

Keywords

Algebraic loop
Commutator
Lie algebra comultiplication
Perturbation

Quacquarelli Symonds(QS) Subject Topics

Computer Science & Information Systems
Mathematics
Chemistry
Physics & Astronomy

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10.3390/SYM12040565

Cite this

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title = "Algebraic inverses on lie algebra comultiplications",

abstract = "In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if l(1)c and r(1)c are the left and right inverses of the identity 1: L → L on a free graded Lie algebra L, respectively, based on the Lie algebra comultiplication ψc: L → L L, then we have l(1) = l(1)c and r(1) = r(1)c, where c: L → L L is a commutator.",

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PY - 2020/4/1

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N2 - In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if l(1)c and r(1)c are the left and right inverses of the identity 1: L → L on a free graded Lie algebra L, respectively, based on the Lie algebra comultiplication ψc: L → L L, then we have l(1) = l(1)c and r(1) = r(1)c, where c: L → L L is a commutator.

AB - In this note, we investigate algebraic loop structures and inverses of elements of a set of all homomorphisms of Lie algebras with a binary operation derived from a Lie algebra comultiplication. As a symmetry phenomenon, we show that if l(1)c and r(1)c are the left and right inverses of the identity 1: L → L on a free graded Lie algebra L, respectively, based on the Lie algebra comultiplication ψc: L → L L, then we have l(1) = l(1)c and r(1) = r(1)c, where c: L → L L is a commutator.

KW - Algebraic loop

KW - Commutator

KW - Lie algebra comultiplication

KW - Perturbation

UR - https://www.scopus.com/pages/publications/85086717349

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DO - 10.3390/SYM12040565

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SN - 2073-8994

VL - 12

JO - Symmetry

JF - Symmetry

IS - 4

M1 - 565

ER -

Algebraic inverses on lie algebra comultiplications

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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