We compute the braided groups and braided matrices B(R) for the solution R of the Yang-Baxter equation associated to the quantum Heisenberg group. We also show that a particular extension of the quantum Heisenberg group is dual to the Heisenberg universal enveloping algebra U q (h), and use this result to derive an action of U q (h) on the braided groups. We then demonstrate the various covaria...

‎in this paper‎, ‎we study translation invariant surfaces in the‎ ‎3-dimensional heisenberg group $rm nil_3$‎. ‎in particular‎, ‎we‎ ‎completely classify translation invariant surfaces in $rm nil_3$‎ ‎whose position vector $x$ satisfies the equation $delta x = ax$‎, ‎where $delta$ is the laplacian operator of the surface and $a$‎ ‎is a $3 times 3$-real matrix‎.

As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...

Odometer actions of discrete, finitely generated and residually finite groups G have been defined by Cortez and Petite. In this paper we focus on the case where G is the discrete Heisenberg group. We prove a structure theorem for finite index subgroups of the Heisenberg group based on their geometry when they are considered as subsets of Z3. We use this structure theorem to provide a classifica...

In this note we describe the embeddings of Heisenberg group into Cremona group.

Let H be the three-dimensional Heisenberg group. We introduce a structure on the Heisenberg group which consists of the biregular representation of H×H restricted to some discrete subset of H×H and a free group of automorphisms H singly generated and acting semi-simply on H. Using well-known theorems borrowed from Gabor theory, we are able to construct simple and computable bandlimited discrete...