The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

Semi-infinite forms on the moduli spaces of genus-zero Riemann surfaces with punctures and local coordinates are introduced. A partial operad for semi-infinite forms is constructed. Using semi-infinite forms and motivated by a partial suboperad of the partial operad for semi-infinite forms, topological vertex partial operads of type k < 0 and strong topological vertex partial operads of type k ...

With every Lie semi-group, Π, possessing certain regularity properties, there is associated a Lie algebra, A; and with every strongly continuous representation of Π in a Banach space there is associated a representation A(a) of A. Certain theorems regarding this representation are established. The above theorems are valid for a representation of a Lie group also. In this case, it is shown that ...

It has been conjectured that the group algebra Q[G] of a discrete group G over the rational numbers Q is semi-simple. In this paper we consider irreducible representations of this algebra satisfying certain finiteness conditions and see just how much information these yield towards solving the above problem. We show in fact for a finitely generated group G, Q[G] has "enough" of these representa...

We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e., quantised enveloping algebra of a simple Lie algebra. For the example, we construct the N =1 and generalized N =2 supersymmetry theory which leads to the Seiberg-W...

The above theorems are valid for a representation of a Lie group also. In this case, it is shown that it is possible to extend the representation to elliptic elements of the universal enveloping algebra. It is also shown that the representatives of the strongly elliptic elements of the universal enveloping algebra are the infinitesimal generators of holomorphic semi-groups. Integral representat...

In this paper, a new notion, called TM-algebra, which is a generalization of the idea of Q/BCH/BCI/BCK/BCC-algebra, is introduced. Some theorems discussed in Q-and BCK algebras are generalized. Definition of TM-algebra along with various propositions are stipulated and presented with their respective proofs. The relation between TM-algebra and other algebra has been investigated and detailed in...

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

this article presents a unified approach to the abstract notions of partial convolution and involution in $l^p$-function spaces over semi-direct product of locally compact groups. let $h$ and $k$ be locally compact groups and $tau:hto aut(k)$ be a continuous homomorphism.  let $g_tau=hltimes_tau k$ be the semi-direct product of $h$ and $k$ with respect to $tau$. we define left and right $tau$-c...

In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra A with constants 0, 1 is Booolean-like in case for all a ∈ A the congruences θ (a, 0) and θ (a, 1) are compementary factor congruences of A. We also introduced the weaker notion of semi-Boolean-like algebra, showin...