Jullien’s indecomposability theorem states that if a scattered countable linear order is indecomposable, then it is either indecomposable to the left, or indecomposable to the right. The theorem was shown by Montalbán to be a theorem of hyperarithmetic analysis. We identify the strength of the theorem relative to standard reverse mathematics markers. We show that it lies strictly between weak Σ...

We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot L [ 1 , … n ] we associate quiver Q with potential and its algebra A . family of canonical indecomposable -modules M ( i ) each supported on different specific subquiver Each the is expected to parametrize Jones polynomial knot. study direct sum = ? these indecomposables inside module category as well i...

We give a complete classification of infinite dimensional indecomposable weight modules over the Lie superalgebra sl(2/1). §1. Introduction Among the basic-classical Lie superalgebras classified by Kac [3], the lowest dimensional of these is the Lie superalgebra B(0, 1) or osp(1, 2), while the lowest dimensional of these which has an isotropic odd simple root is the Lie superalgebra A(1, 0) or ...

For each simply-laced Dynkin graph ∆ we realize the simple complex Lie algebra of type ∆ as a quotient algebra of the complex degenerate composition Lie algebra L(A) 1 of a domestic canonical algebra A of type ∆ by some ideal I of L(A) 1 that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of L(A) 1 /I has a basis given by the coset o...

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i. e. for fusion categories), obtained recently in our joint work with D. Nikshych. In particular, we generalize to the categorical setting the Hopf and quasi-Hopf algebra freeness theorems due to Nichols–Zoeller and Schauenburg, respectively. We also gi...

Let G be a finite group of Lie type of characteristic p, and k a sufficiently large field of the same characteristic. The permutation module Y=ind,.(k) on the right cosets of a Sylow p-subgroup tJ has been studied by several authors; the fundamental results are due to Curtis and Richen (see [S], whose used the module Y to describe the irreducible kG-modules. Later their results were reinterpret...