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On certain Hecke rings.

S Evens¹, P Bressler

¹Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139.

Proceedings of the National Academy of Sciences of the United States of America

|February 1, 1987

Summary

This study investigates specific rings within algebraic structures related to Weyl groups. Researchers proved these rings are isomorphic to known algebraic structures like the Hecke algebra or nil Hecke ring.

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Area of Science:

Algebraic Topology
Representation Theory
Abstract Algebra

Background:

The study of rings and their properties is fundamental in abstract algebra.
Weyl groups and their associated algebras are crucial in understanding symmetries in mathematics and physics.
Braid relations appear in various areas, including knot theory and quantum groups.

Purpose of the Study:

To classify rings embedded within the smash product of a Weyl group algebra and meromorphic functions.
To determine the structure of rings generated by elements satisfying braid relations.

Main Methods:

The research involves examining the structure of specific rings within a defined algebraic construction.
Key methods include utilizing properties of the smash product and braid relations.

Main Results:

The study proves that rings generated by elements satisfying braid relations are isomorphic to one of three specific algebraic structures.
These structures are identified as the Hecke algebra, the nil Hecke ring, or the group algebra of the Weyl group.

Conclusions:

The classification provides a comprehensive understanding of the rings under investigation.
This result contributes to the broader study of algebraic structures and their interrelations.

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