We present an explicit conjecture for the chiral fusion algebra of critical percolation considering Virasoro representations with no enlarged or extended symmetry algebra. The representations we take to generate fusion are countably infinite in number. The ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of these representations decomposes into a finite di...

We show that universal algebras with factorable congruences such as rings with 1 and semirings with 0 and 1 enjoy some of the properties of universal algebras whose congruence lattices are distributive, such as the strict refinement property and a variant of Jónsson’s lemma. A universal algebra A is said to have factorable congruences if whenever A ∼= B × C and θ is a congruence on A, then θ = ...

We present explicit conjectures for the chiral fusion algebras of the logarithmic minimal models LM(p, p ′) considering Virasoro representations with no enlarged or extended symmetry algebra. The generators of fusion are countably infinite in number but the ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of representations decomposes into a finite direct ...

We introduce the notions of τ -exceptional and signed sequences for any finite dimensional algebra. prove that a fixed algebra rank n , positive integer t ≤ there is bijection between set length (basic) ordered support -rigid objects with indecomposable direct summands. If hereditary, our coincide exceptional sequences. The latter were recently introduced by Igusa Todorov, who constructed simil...

By using the approach to Hall algebras arising in homologically finite triangulated categories in [9], we find an “almost” associative multiplication structure for indecomposable objects in a 2-period triangulated category. As an application, we give a new proof of the theorem of Peng and Xiao in [6] which provides a way of constructing all symmetrizable Kac-Moody Lie algebras from two periodic...

Based on symmetry principles, we derive a fusion algebra generated from repeated fusions of the irreducible modules appearing in the W-extended logarithmic minimal model WLM(p, p′). In addition to the irreducible modules themselves, closure of the commutative and associative fusion algebra requires the participation of a variety of reducible yet indecomposable modules. We conjecture that this f...

Based on symmetry principles, we derive a fusion algebra generated from repeated fusions of the irreducible modules appearing in the W-extended logarithmic minimal model WLM(p, p′). In addition to the irreducible modules themselves, closure of the commutative and associative fusion algebra requires the participation of a variety of reducible yet indecomposable modules. We conjecture that this f...

It is proved that an irreducible quasifinite W∞-module is a highest or lowest weight module or a module of the intermediate series; a uniformly bounded indecomposable weight W∞module is a module of the intermediate series. For a nondegenerate additive subgroup Γ of F, where F is a field of characteristic zero, there is a simple Lie or associative algebra W(Γ, n)(1) spanned by differential opera...