Computer Algebra of Vector Bundles, Foliations and Zeta Functions and a Context of Noncommutative Geometry

نویسنده

  • Nikolaj M. Glazunov
چکیده

We present some methods and results in the application of algebraic geometry and computer algebra to the study of algebraic vector bundles, foliations and zeta functions. A connection of the methods and results with noncommutative geometry will be consider.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Topology of the C*{algebra bundles

Using the methods of the noncommutative geometry and the K–theory, we prove that the well–known Dixmier–Douady invariant of continuous–trace C –algebras and the Godbillon– Vey invariant of the codimension–1 foliations on compact manifolds coincide in a class of the so–called ”foliation derived” C–algebra bundles. Moreover, with the help of such bundles both of the above invariants admit an eleg...

متن کامل

Noncommutative generalization of SU(n)-principal ber bundles: a review

This is an extended version of a communication made at the international conference Noncommutative Geometry and Physics held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary ber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its di erential calculus is based on its Lie...

متن کامل

Noncommutative Geometry Year 2000

Our geometric concepts evolved first through the discovery of NonEuclidean geometry. The discovery of quantum mechanics in the form of the noncommuting coordinates on the phase space of atomic systems entails an equally drastic evolution. We describe a basic construction which extends the familiar duality between ordinary spaces and commutative algebras to a duality between Quotient spaces and ...

متن کامل

Derivations of the Algebra of Sections of Superalgebra Bundles

In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...

متن کامل

Lessons from Quantum Field Theory Hopf Algebras and Spacetime Geometries

We discuss the prominence of Hopf algebras in recent progress in Quantum Field Theory. In particular, we will consider the Hopf algebra of renormalization, whose antipode turned out to be the key to a conceptual understanding of the subtraction procedure. We shall then describe several occurences of this, or closely related Hopf algebras, in other mathematical domains, such as foliations, Runge...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2001