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Quantum cluster algebras and quantum nilpotent algebras.

• Kenneth R Goodearl, Milen T Yakimov
• Proceedings of the National Academy of Sciences…
• 2014

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We… (More)

POISSON STRUCTURES ON AFFINE SPACES AND FLAG VARIETIES . II . GENERAL CASE

• Kenneth R Goodearl
• 2005

The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal… (More)

Explorer Totally nonnegative cells and matrix Poisson varieties

• Kenneth R Goodearl, Stéphane Launois, T. Lenagan
• 2009

We describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices, that is, the families of minors that produce nonempty cells in the cell decompositions of… (More)

Representations of Distributive Semilattices by Dimension Groups, Regular Rings, C*-algebras, and Complemented Modular Lattices

• Kenneth R Goodearl, E. Tamás Schmidt
• 2001

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neu-mann regular rings, C*-algebras, and complemented modular… (More)

The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group

• Kenneth R Goodearl, T. Lenagan, Laurent Rigal
• 2005

We prove First Fundamental Theorems of Coinvariant Theory for the standard coactions of the quantum groups Oq(GLt(K)} and (9q(SLt(K}) on the quantized algebra &q(Mm,t(K)) <g> Gq(Mt,n(K)). (Here K is… (More)

PRIME IDEALS INVARIANT UNDER WINDING AUTOMORPHISMS IN QUANTUM MATRICES K. R. Goodearl and T. H. Lenagan

• Kenneth R Goodearl, T. Lenagan
• 2001

A −→ A⊗ A −→ A ⊗A− −→ (A/P)⊗ (A−/P−) where A → A ⊗ A is the comultiplication, A+ and A− are suitable localized factor algebras of A, and P± is a prime ideal of A± invariant under winding… (More)

K0 OF PURELY INFINITE SIMPLE REGULAR RINGS

• Kenneth R Goodearl, Enrique Pardo
• 2014

We extend the notion of a purely infinite simple C*-algebra to the context of unital rings, and we study its basic properties, specially those related to K-Theory. For instance, if R is a purely… (More)

THE ALMOST ISOMORPHISM RELATION FOR SIMPLE REGULAR RINGS

• Pere Ara, Kenneth R Goodearl
• 2006

A longstanding open problem in the theory of von Neumann regular rings is the question of whether every directly finite simple regular ring must be unit-regular. Recent work on this problem has been… (More)

Semilattices of groups and inductive limits of Cuntz algebras

• Kenneth R Goodearl
• 2005

We characterize, in terms of elementary properties, the abelian monoids which are direct limits of finite direct sums of monoids of the form (Z/nZ)⊔{0} (where 0 is a new zero element), for positive… (More)

Pacific Journal of Mathematics K 1 OF SEPARATIVE EXCHANGE RINGS AND C *-ALGEBRAS WITH REAL RANK ZERO

• Pere Ara, Kenneth R Goodearl, K. C. O’Meara, Richard Raphael
• 2006

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