Volume 31, Issue 3
Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$

Yu-E Zhao

Commun. Math. Res., 31 (2015), pp. 229-241.

Published online: 2021-05

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  • Abstract

In this paper, through a meticulous description of finite root system, a concrete comultiplication with an explicit action on the basis elements of finite dimensional simple Lie algebras of type $A$, $D$, $E$ is constructed. Then any finite dimensional simple Lie algebra of type $A$, $D$, $E$ is endowed with a new generalized Lie coalgebra splitting. This construction verifies the known existence of a co-split Lie structure on any finite dimensional complex simple Lie algebra.

  • Keywords

Lie coalgebra, co-splitting, finite-dimensional simple Lie algebra.

  • AMS Subject Headings

17B62, 17B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-31-229, author = {Zhao , Yu-E}, title = {Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {3}, pages = {229--241}, abstract = {

In this paper, through a meticulous description of finite root system, a concrete comultiplication with an explicit action on the basis elements of finite dimensional simple Lie algebras of type $A$, $D$, $E$ is constructed. Then any finite dimensional simple Lie algebra of type $A$, $D$, $E$ is endowed with a new generalized Lie coalgebra splitting. This construction verifies the known existence of a co-split Lie structure on any finite dimensional complex simple Lie algebra.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.03.05}, url = {http://global-sci.org/intro/article_detail/cmr/18925.html} }
TY - JOUR T1 - Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$ AU - Zhao , Yu-E JO - Communications in Mathematical Research VL - 3 SP - 229 EP - 241 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.03.05 UR - https://global-sci.org/intro/article_detail/cmr/18925.html KW - Lie coalgebra, co-splitting, finite-dimensional simple Lie algebra. AB -

In this paper, through a meticulous description of finite root system, a concrete comultiplication with an explicit action on the basis elements of finite dimensional simple Lie algebras of type $A$, $D$, $E$ is constructed. Then any finite dimensional simple Lie algebra of type $A$, $D$, $E$ is endowed with a new generalized Lie coalgebra splitting. This construction verifies the known existence of a co-split Lie structure on any finite dimensional complex simple Lie algebra.

Yu-E Zhao. (2021). Co-Splitting of Simple Lie Algebras of Type $A$, $D$, $E$. Communications in Mathematical Research . 31 (3). 229-241. doi:10.13447/j.1674-5647.2015.03.05
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