The Lie groupoid analogue of a symplectic Lie group

A symplectic Lie group is a with left-invariant form. Its algebra structure that of quasi-Frobenius algebra. In this note, we identify the groupoid analogue group. We call aforementioned \textit{$t$-symplectic groupoid}; $t$ motivated by fact each target fiber $t$-symplectic manifold. For $\mathcal{G}\rightrightarrows M$, show there one-to-one correspondence between algebroid structures on $A\mathcal{G}$ (the associated algebroid) and M$. addition, also introduce notion \textit{symplectic bundle} (SLGB) which special case both bundle. The basic properties SLGBs are explored.