Contact forms on SL(2p)

TL;DR

This paper investigates invariant contact forms on the Lie group SL(2p), showing that while left invariant forms are not contact forms for p>1, a specific SO(2p)-invariant contact form exists.

Contribution

The paper demonstrates the non-existence of left invariant contact forms on SL(2p) for p>1 and constructs an SO(2p)-invariant contact form, highlighting new invariant structures.

Findings

Left invariant Pfaffian forms are not contact forms on SL(2p) for p>1.

An SO(2p)-invariant contact form on SL(2p) is explicitly constructed.

The invariance properties of contact forms on SL(2p) are clarified.

Abstract

When p is greater than 1, any left invariant Pfaffian forms on the simple Lie group SL(2p) are not contact forms. In this paper, we give a contact form on this Lie group which is invariant by the subgroup SO(2p).