We construct geometrically the generating fields of a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes X [n] of n points on a projective surface X for all n ≥ 0. We compute explicitly the commutators among the Fourier components of the generating fields of the W algebra, and identify this algebra with a W1+∞-type algebra. A precise formula of cer...

We construct two possible candidates for the non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. The bms4 algebra is infinitedimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinitedimensional extensions...

For locally compact groups Gi, i = 1, 2, · · · , n, let CB(G1, · · · , Gn) denote the Banach space of completely bounded multilinear forms on C0(G1)×· · ·×C0(Gn) in the completely bounded norm. CB(G1, · · · , Gn) has the structure of a Banach ∗-algebra under a multiplication and adjoint operation which agree with the convolution structure on the measure algebra M(G1 ×· · ·×Gn). If the Gi are al...

We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra ...

Using the notion of a symmetric virtual diagonal for Banach algebra, we prove that algebra is symmetrically amenable if its second dual amenable. We introduce operator amenability in category completely contractive algebras as an analogue algebras. give some equivalent formulations and investigate hereditary properties show locally compact groups to Fourier algebra. Finally, discuss about Jorda...