We show that amenability, the Haagerup property, the Kazhdan´s property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of ...

We define and study coherent states, a Berezin-Toeplitz quantization and covariant symbols on the product Xi := G x g(#) between a connected simply connected nilpotent Lie group and the dual of its Lie algebra. The starting ...

In this paper we give a description of all eight-dimensional simply connected nilpotent Lie groups carrying a left invariant hypercomplex structure.

For a real, non-singular, 2-step nilpotent Lie algebra n, the group Aut(n)/ Aut0(n), where Aut0(n) is the group of automorphisms which act trivially on the center, is the direct product of a compact group with the 1-dimensional ...

Let N be a nilpotent Lie group and K a compact subgroup of the automorphism group Aut(N) of N. It is well-known that if (K⋉ N, K) is a Gelfand pair then N is at most 2-step nilpotent Lie group. The notion of Gelfand pair ...

We describe the set of all locally nilpotent derivations of the quotient ring K[X,Y, Z]/(f (X)Y - phi(X, Z)) constructed from the defining equation f (X)Y = phi(X, Z) of a generalized Danielewski surface in K-3 for a ...

In this article we study nonassociative rings satisfying the polynomial identity x yz = y zx , which we call “cyclic rings.” We prove that every semiprime cyclic ring is associative and commutative and that every cyclic ...

In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing–Yano 2-form are the complex Lie groups. In the case of 2-step nilpotent complex Lie groups arising from ...