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 - <p style="text-align: justify;">In this article, we study the Lie supertriple system (LSTS) $T$ over a field&nbsp;$\mathbb{K}$ 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 &quot;same&quot;, i.e.,
they are equivalent or isometrically equivalent.</p>