Volume 30, Issue 1
$T^∗$-Extension of Lie Supertriple Systems

Commun. Math. Res., 30 (2014), pp. 51-59.

Published online: 2021-05

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• Abstract

In this article, we study the Lie supertriple system (LSTS) $T$ over a field $\mathbb{K}$ admitting a nondegenerate invariant supersymmetric bilinear form (call such a $T$ metrisable). We give the definition of $T^∗_ω$-extension of an LSTS $T$, prove a necessary and sufficient condition for a metrised LSTS ($T$, $ϕ$) to be isometric to a $T^∗$-extension of some LSTS, and determine when two $T^∗$-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.

• Keywords

pseudo-metrised Lie supertriple system, metrised Lie supertriple system, $T^∗$-extension.

17A40, 17B05

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@Article{CMR-30-51, author = {Feng , Jianqiang}, title = {$T^∗$-Extension of Lie Supertriple Systems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {1}, pages = {51--59}, abstract = {

In this article, we study the Lie supertriple system (LSTS) $T$ over a field $\mathbb{K}$ admitting a nondegenerate invariant supersymmetric bilinear form (call such a $T$ metrisable). We give the definition of $T^∗_ω$-extension of an LSTS $T$, prove a necessary and sufficient condition for a metrised LSTS ($T$, $ϕ$) to be isometric to a $T^∗$-extension of some LSTS, and determine when two $T^∗$-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/18987.html} }
TY - JOUR T1 - $T^∗$-Extension of Lie Supertriple Systems AU - Feng , Jianqiang JO - Communications in Mathematical Research VL - 1 SP - 51 EP - 59 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/18987.html KW - pseudo-metrised Lie supertriple system, metrised Lie supertriple system, $T^∗$-extension. AB -

In this article, we study the Lie supertriple system (LSTS) $T$ over a field $\mathbb{K}$ admitting a nondegenerate invariant supersymmetric bilinear form (call such a $T$ metrisable). We give the definition of $T^∗_ω$-extension of an LSTS $T$, prove a necessary and sufficient condition for a metrised LSTS ($T$, $ϕ$) to be isometric to a $T^∗$-extension of some LSTS, and determine when two $T^∗$-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.

Jianqiang Feng. (2021). $T^∗$-Extension of Lie Supertriple Systems. Communications in Mathematical Research . 30 (1). 51-59. doi:
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