Related papers: Weakly primitive axial algebras
Axial algebras are non-associative algebras generated by semisimple idempotents, known as axes, that all obey a fusion rule. Axial algebras were introduced by Hall, Rehren and Shpectorov as a generalisation of the axioms of Majorana theory,…
This is a study of weakly integral braided fusion categories with elementary fusion rules to determine which possess nondegenerately braided extensions of theoretically minimal dimension, or equivalently in this case, which satisfy the…
Poly-bicategories generalise planar polycategories in the same way as bicategories generalise monoidal categories. In a poly-bicategory, the existence of enough 2-cells satisfying certain universal properties (representability) induces…
A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved…
Using the natural action of $S_\infty$ we show that a countable hereditary class $\mathcal C$ of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a…
The behaviour of limits of weak morphisms in 2-dimensional universal algebra is not 2-categorical in that, to fully express the behaviour that occurs, one needs to be able to quantify over strict morphisms amongst the weaker kinds.…
Specializing properly the parameters contained in the maximal cyclic representation of the non-restricted A-type quantum algebra at roots of unity, we find the unique primitive vector in it. We show that the submodule generated by the…
The paper is devoted to the study of finite dimensional complex evolution algebras. The class of evolution algebras isomorphic to evolution algebras with Jordan form matrices is described. For finite dimensional complex evolution algebras…
In this survey article we outline the history of the twin theories of weak normality and seminormality for commutative rings and algebraic varieties with an emphasis on the recent developments in these theories over the past fifteen years.…
We say that a ring is strongly (resp. weakly) left Jacobson if every semiprime (resp. prime) left ideal is an intersection of maximal left ideals. There exist Jacobson rings that are not weakly left Jacobson, e.g. the Weyl algebra. Our main…
The class of weak BCK-algebras is obtained by weakening one of standard BCK axioms. It is known that every weak BCK-algebra is completely determined by the structure of its initial segments. We review several natural classes of commutative…
We introduce the notion of (nondegenerate) strong-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group SL(2,Z) whose kernel contains a…
In this paper, we first show for a slightly degenerate pre-modular fusion category $\mathcal{C}$ that squares of dimensions of simple objects divide half of the dimension of $\mathcal{C}$, and that slightly degenerate fusion categories of…
A finite-dimensional algebra $A$ over an algebraically closed field $K$ is called periodic if it is periodic under the action of the syzygy operator in the category of $A-A-$ bimodules. The periodic algebras are self-injective and occur…
Bartholdi and Smoktunowicz constructed finitely generated monomial algebras with prescribed sufficiently fast growth types. We show that their construction need not result in a prime algebra, but it can be modified to provide prime algebras…
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities $a(bc) = a(cb)$, $(ba)a^2 = (ba^2)a$, and $(b,a^2,c) = 2(b,a,c)a$. These identities are satisfied by the product $ab = a \dashv b + b…
Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those…
In this paper we prove that any Poisson structure on a sheaf of Lie algebroids admits a weak deformation quantization, and give a sufficient condition for such a Poisson structure to admit an actual deformation quantization. We also answer…
The constraints proposed recently by Bershadsky to produce $W^l_n$ algebras are a mixture of first and second class constraints and are degenerate. We show that they admit a first-class subsystem from which they can be recovered by…
In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures, which we call Poisson fibred algebras, appear in the study of quantum groups at…