in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

the paper deal with non-commutative geometry. the notion of quantumspheres was introduced by podles. here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

Let Λ be a ring endowed with an involution a 7→ ã. We say that two units a and b of Λ fixed under the involution are congruent if there exists an element u ∈ Λ× such that a = ubũ. We denote by H(Λ) the set of congruence classes. In this paper we consider the case where Λ is an order with involution in a semisimple algebraA over a local field and study the question whether the natural map H(Λ)→ ...

This article is concerned with the study of the geometry of determinant line bundles associated to families of spectral triples parametrized by the moduli space of gauge equivalence classes of Hermitian connections on a Hermitian finite projective module. We illustrate our results with some examples that arise in noncommutative geometry. Mathematics Subject Classification (2000). 58B34; 46L87, ...

We show the compatibility between the moderate or nearby cycle functor for regular holonomic D-modules, as defined by Beilinson, Kashiwara and Malgrange, and the Hermitian duality functor, as defined by Kashiwara. Introduction The Hermitian dual of a D-module was introduced by M. Kashiwara in [9], who showed that the Hermitian dual of a regular holonomic D-module is also regular holonomic (henc...

We describe a nonsingular hermitian form of rank 4 over the group ring Z[Z] which is not extended from the integers. Moreover, we show that under certain indefiniteness asumptions, every nonsingular hermitian form on a free Z[Z]module is extended from the integers. As a corollary, there exists a closed oriented 4-dimensional manifold with fundamental group Z which is not the connected sum of S ...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficients in the “current” module, and apply them to compute structure functions for manifolds of loops with values in compact Hermitian symmetric spaces.

We obtain formulas for the first and second cohomology groups of a general current Lie algebra with coefficient in the “current” module, and apply them to computation of structure functions associated with manifolds of loops on compact Hermitian symmetric space.

Let f! = G/K be a symmetric tube domain where G is the universal cover of Aut(f!). Let X be a line bundle on the Shilov boundary, and let I(x) be the space of sections. This paper determines (a) the composition series for I(x) as a ({1, K)module, (b) the K-module structure of each constituent, (c) explicit formulas for possible invariant Hermitian forms on these constituents, and (d) the unitar...