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In this paper we state and prove the analogous of the principal ideal theorem of algebraic number theory for the case of 3-manifolds from the point of view of arithmetic topology.
We give the classification of 3-dimensional Bol algebras associated to the trilinears operations $(e_2,e_3, e_2)=e_1, (e_2, e_3, e_3)=\pme_2$. It turn that for such trilinears operation there exist up to isomorphism and isotopy one family…
We determine the representations of the Yokonuma-Temperley-Lieb algebra, which is defined as a quotient of the Yokonuma-Hecke algebra by generalising the construction of the classical Temperley-Lieb algebra. We then deduce the dimension of…
Using the notion of passport of a normed Boolean algebra, necessary and sufficient conditions for a $\ast$-isomorphism of $\ast$-algebras of log-integrable measurable functions are found.
Let $K$ be a normal subgroup of the finite group $H$. To a block of a $K$-interior $H$-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to a block given by the Brauer…
The recollement approach to the representation theory of sequences of algebras is extended to pass basis information directly through the globalisation functor. The method is hence adapted to treat sequences that are not necessarily towers…
This article examines the growth of generalized algebras of type Temperley-Lieb $ TL _ {\ Gamma, \ tau}. $ Studied them dimension or if the algebra of infinite growth.
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to…
Techniques from representation theory, symbolic computational algebra, and numerical algebraic geometry are used to find the minimal generators of the ideal of the trifocal variety. An effective test for determining whether a given tensor…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
We prove that any derived equivalence between triangular algebras is standard, that is, it is isomorphic to the derived tensor functor given by a two-sided tilting complex.
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
A description of group automorphisms of all two-dimensional algebras, considered up to isomorphism, over any basic field is provided.
We introduce stability categories for diagram algebras---analogues to Randal-Williams and Wahl's homogeneous categories. We use these to study representation stability properties of the Temperley--Lieb algebras, the Brauer algebras, and the…
This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.
Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying…
We prove that any derived equivalence between derived discrete algebras is standard, i.e.\ is isomorphic to the derived tensor product by a two-sided tilting complex.
We determine all values of the parameters for which the cell modules form a standard system, for a class of cellular diagram algebras including partition, Brauer, walled Brauer, Temperley-Lieb and Jones algebras. For this, we develop and…
In this paper, we present an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley--Lieb algebra having a basis indexed by the fully commutative elements (in the sense of Stembridge) of…