On some approaches towards non-commutative algebraic geometry

Details On some approaches towards non-commutative algebraic geometry On some approaches towards non-commutative algebraic geometry

2005-01-11

arxiv.org/abs/math/0501166v5

Mathematics

Quantum Algebra

55 pages, some revisions made, misprints removed and references added

Scientific paper

The works of R. Descartes, I. M. Gelfand and A. Grothendieck have convinced us that commutative rings should be thought of as rings of functions on some appropriate (commutative) spaces. If we try to push this notion forward we reach the realm of Non-commutative Geometry. The confluence of ideas comes here mainly from three seemingly disparate sources, namely, quantum physics, operator algebras (Connes-style) and algebraic geometry. Following the title of the article, an effort has been made to provide an overview of the third point of view. Since na\" ive efforts to generalize commutative algebraic geometry fail, one goes to the root of the problem and tries to work things out "categorically". This makes the approach a little bit abstract but not abstruse. However, an honest confession must be made at the outset - this write-up is very far from being definitive; hopefully it will provide glimpses of some interesting developments at least.

Affiliated with

Also associated with

No associations

Rating

On some approaches towards non-commutative algebraic geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On some approaches towards non-commutative algebraic geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On some approaches towards non-commutative algebraic geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-201978