The prime spectra of two families of algebras, Sw and Šw, w ∈ W, indexed by the Weyl group W of a semisimple finitely dimensional Lie algebra g, are studied in the spirit of [J3]. The algebras Sw have been introduced by A. Joseph (see [J4], Sect. 3). They are q-analogues of the algebras of regular functions on w-translates of the open Bruhat cell of a semisimple Lie group G corresponding to the...

We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra ha...

1 Introduction. We consider the class of Noetherian ring, appeared as a result of quantization of algebraic groups and their representations within framework of mathematical physics. One set up the problem of description of prime and primitive spectrum of these rings. This problem has been solved first for algebras of low dimension , then for the case GL q (n), later for general case of regular...

Article history: Received 28 June 2012 Revised 2 December 2012 Accepted 10 January 2013 Available online 31 January 2013 Communicated by Gary McGuire

This paper is a companion to the Boardman–Wilson paper on the ring spectrum P (n). When the prime is 2, this spectrum is not commutative, which introduces several complications. Here, we supply the necessary details of the relevant Hopf algebroids and Hopf ring for this case.

We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated by a recent study of the optical absorption spectrum of a graded metallic film [Huang and Yu, Appl. Phys. Lett. 85, 94 (2004)] in which a broad surface-plasmo...

We fix a base field k of characteristic not dividing l. We suppose that k contains a primitive l-th root of unity ζ , and fix it. Starting from these data, one defines certain category C. Its objects are finite dimensional X-graded k-vector spaces equipped with an action of Lusztig’s ”small” quantum group u (cf. [L2]) such that the action of its Cartan subalgebra is compatible with the X-gradin...

We develop the theory of “branch algebras”, which are infinitedimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting on trees. In particular, for every field k we construct a k-algebra K which • is finitely generated and infinite-dimensional, but has only finite-dimensional qu...

Motivated by a recent conjecture by Hernandez and Leclerc [30], we embed a Fomin-Zelevinsky cluster algebra [20] into the Grothendieck ring R of the category of representations of quantum loop algebras Uq(Lg) of a symmetric Kac-Moody Lie algebra, studied earlier by the author via perverse sheaves on graded quiver varieties [48]. Graded quiver varieties controlling the image can be identified wi...

We show that any quasi-Gorenstein deformation of a 3-dimensional Buchsbaum local ring with I-invariant 1 admits maximal Cohen-Macaulay module, provided it is quotient Gorenstein ring. Such class rings includes two instances unique factorization domains constructed by Marcel-Schenzel and Imtiaz-Schenzel, respectively. Apart from this result, motivated the small conjecture in prime characteristic...