The heat kernel on the Cayley Heisenberg group (Q815132)

The authors obtain an explicit expression for the heat kernel for the Cayley group of order \(n\) using the stochastic integral method of Gaveau. This expression for the heat kernel resembles the heat kernel for the Heisenberg group. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, the Cayley group of order \(n\) is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.