Recent development of string theory has shown that noncommutative (NC) models can arise in certain limits of String Theory [1]. Moreover the String Field Theory [2], which is the theory of second quantised string, is based on noncommutative geometry too. Due to their proximity to String Theory noncommutative theories have many features in common with it. It is worthwhile to mention the IR/UV mi...

Even if one is interested only in finite-dimensional manifolds, the need for infinitedimensional manifolds sometimes arises. For example, one approach to study closed geodesics on a manifold is to use Morse theory on its (free) loop space; while for some purposes it is enough to work with finite-dimensional approximations, it is helpful for some finer aspects of the theory to use models of the ...

We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D = 11 supergravity theory to two space-time dimensions in the context of hidden Kac–Moody symmetries. The action of the resulting infinitedimensional ‘R symmetry’ group K(E9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E10) is studied. We explain in detail...

One can prove the following two propositions: (1) Let V be a real unitary space, A, B be finite subsets of V , and v be a vector of V . Suppose v ∈ Lin(A∪B) and v / ∈ Lin(B). Then there exists a vector w of V such that w ∈ A and w ∈ Lin(((A ∪ B) \ {w}) ∪ {v}). (2) Let V be a real unitary space and A, B be finite subsets of V . Suppose the unitary space structure of V = Lin(A) and B is linearly ...

It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite dimensional unstable manifolds. In this article, these results are unified to show that for a specific parabolic equation on an unbounded domain, the space of hete...

We show that each reflexive finite-dimensional subspace of operators is hyperreflexive. This gives a positive answer to a problem of Kraus and Larson. We also show that each n– dimensional subspace of Hilbert space operators is [ √ 2n]–hyperreflexive.

We give a general construction of affine noetherian algebras with the property that every finite dimensional representation is completely reducible. Starting from enveloping algebras of semi simple Lie algebras in characteristic zero we obtain explicit examples and describe some of their properties. In the following an algebra A will always mean an associative algebra over a field k with a unit...

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

For a left vector space V over a totally ordered division ring F, let Co(V ) denote the lattice of convex subsets of V . We prove that every lattice L can be embedded into Co(V ) for some left F-vector space V . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form Co(V,Ω) = {X ∩Ω | X ∈ Co(V )}, for some f...