nLab Claus Michael Ringel

Claus Michael Ringel is a German algebraist.

• personal page

Selected work

On Hall algebras:

• Claus M. Ringel, The Hall multiplication], lecture notes (2006) [web]

Ringel realized that Hall's construction of an associative algebra structure from the combinatorics of flags of p-abelian groups (defined in terms of numbers of extensions) can be applied to the category of representations of a quiver over a finite field $\mathbf{F}_q$ and related it to quantum groups in

• C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (3): 583–591, doi MR1062796
• wikipedia: Ringel-Hall algebra

This work influenced George Lusztig‘s work on quantum groups where Lusztig has constructed “the upper half” of quantum group as a Hall algebra adapted to perverse sheaves over flag variety of a quiver.

On Artin algebras:

• Claus Michael Ringel; section 1 of: On the representation dimension of Artin algebras [pdf]

Other works:

• C. M. Ringel, The simple Artinian spectrum of a finite dimensional algebra (in Dekker Lect. Notes 51, 1979)

category: people