We consider the string, like point particles and branes, to be an irreducible representation of semi-direct product Cartan involution invariant subalgebra [Formula: see text] its vector representation. show that preserves string charges, little algebra, is essentially Borel text]. also known physical states carry a parts this algebra.

In this paper, we begin to study the subalgebra lattice of a Leibniz algebra. particular, deal with algebras whose is modular, upper semi-modular, lower distributive, or dually atomistic. The fact that non-Lie algebra has fewer one-dimensional subalgebras in general results number conditions being weaker than Lie case.

In this paper we define infinite-dimensional algebra and its representation, whose basis is naturally identified with semi-infinite configurations of the square ladder model (square lattice two lines). All these lead to representation N=2 algebra. We also extrapolate ideas for 3-leg triangular on cylinder.

Introduction. Let A be a commutative semi-simple Banach algebra and let A(.4) be the set of nonzero multiplicative functionals on A. Denote by A' the strongly closed span of A(^4) and by A" the Banach space adjoint of A'. Modifying a construction of R. Arens [l] we introduce a multiplication in A" under which A" becomes a commutative Banach algebra. A is algebraically isomorphic to a subalgebra...

Let A be a separable C∗-algebra and let B be a stable C∗-algebra with a strictly positive element. We consider the (semi)group Ext(A,B) (resp. Ext(A,B)) of homotopy classes of asymptotic (resp. of genuine) homomorphisms from A to the corona algebra M(B)/B and the natural map i : Ext(A,B) −→ Ext(A,B). We show that if A is a suspension then Ext(A,B) coincides with E-theory of Connes and Higson an...

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic Poisson superpairs over a semi-finitely-filtered polarized Z2-graded associative algebra. Then we give a construction of certain Hamiltonian superpairs in t...

Local effective action is derived to describe Regge asymptotic of Yang–Mills theories. Local symmetries of the effective action originating from the gauge symmetry of the underlying Yang–Mills theory are studied. Multicomponent effective action is introduced to express the symmetry transformations as field transformations. The algebra of these symmetries is decomposed onto a semi-direct sum of ...