Proceedings of the National Academy of Sciencesâ€¦

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. Weâ€¦ (More)

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 maximalâ€¦ (More)

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 ofâ€¦ (More)

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 modularâ€¦ (More)

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 isâ€¦ (More)

A âˆ’â†’ AâŠ— A âˆ’â†’ A âŠ—Aâˆ’ âˆ’â†’ (A/P)âŠ— (Aâˆ’/Pâˆ’) where A â†’ A âŠ— A is the comultiplication, A+ and Aâˆ’ are suitable localized factor algebras of A, and PÂ± is a prime ideal of AÂ± invariant under windingâ€¦ (More)

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 purelyâ€¦ (More)

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 beenâ€¦ (More)

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)âŠ”{0} (where 0 is a new zero element), for positiveâ€¦ (More)