Related papers: Ideals in Deligne's category Rep(GL_\delta)

We describe indecomposable objects in Deligne's category $\underline{\operatorname{Re}}\!\operatorname{p}(O_\delta)$ and explain how to decompose their tensor products. We then classify thick ideals in…

We derive several tools for classifying tensor ideals in monoidal categories. We use these results to classify tensor ideals in Deligne's universal categories RepO, RepGL and RepP. These results are then used to obtain new insight into the…

We classify indecomposable summands of mixed tensor powers of the natural representation for the general linear supergroup up to isomorphism. We also give a formula for the characters of these summands in terms of composite supersymmetric…

We give new interpretations of the Deligne categories $\underline{Rep}(GL_t)$ and $\underline{Rep}(S_t)$ (and their abelian envelopes) over $\mathbb{C}$ in terms of modular representations of general linear and symmetric groups of large…

We prove a universal property of Deligne's category $\uRep^{ab}(S_d)$. Along the way, we classify tensor ideals in the category $\uRep(S_d)$.

For each integer $t$ a tensor category $V_t$ is constructed, such that exact tensor functors $V_t \longrightarrow C$ classify dualizable $t$-dimensional objects in $C$ not annihilated by any Schur functor. This means that $V_t$ is the…

Let V be an infinite-dimensional vector space over a field of characteristic not equal to 2. We classify ideals of the Lie algebra gl(V) of all linear transformations of the space V.

Recently P. Deligne introduced the tensor category Rep(S_t) (for t not necessarily an integer) which in a certain precise sense interpolates the categories Rep(S_d) of representations of the symmetric groups S_d. In this paper we describe…

We classify simple associative and Lie algebras inside the Deligne categories $Rep(S_t)$, answering a question posed by Etingof.

We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generated by powers of linear generic forms of the corresponding…

In this paper, we introduce the concept of ideal on CL-algebra. It is proved that this concept generalizes the notion of ideal on Residuated Lattices. Prime ideal on CL-algebra are defined and few interesting properties are obtained. It has…

We construct a faithful categorical representation of an infinite Temperley-Lieb algebra on the periplectic analogue of Deligne's category. We use the corresponding combinatorics to classify thick tensor ideals in this periplectic Deligne…

A constructive procedure is given to determine all ideals of a solvable Lie algebra. This is used in determining algorithmically all conjugacy classes of subalgebras of a given solvable Lie algebra.

Starting from an abelian category A such that every object has only finitely many subobjects we construct a semisimple tensor category T. We show that T interpolates the categories Rep(Aut(p),K) where p runs through certain projective…

This paper is a sequel to arXiv:1401.6321. We define and study representation categories based on Deligne categories Rep(GL_t), Rep(O_t), Rep(Sp_2t), where t is any (non-integer) complex number. Namely, we define complex rank analogs of the…

We show that in the Deligne categories $\mathrm{Rep}(S_t)$ for $t$ a transcendental number, the only simple algebra objects are images of simple algebras in the category of representations of a symmetric group under a canonical induction…

Consider a grade 2 perfect ideal $I$ in $R=k[x_1,\cdots,x_d]$ which is generated by forms of the same degree. Assume that the presentation matrix $\varphi$ is almost linear, that is, all but the last column of $\varphi$ consist of entries…

In this article we investigate the distribution of prime ideals of residue degree bigger than one across the ideal classes in the class group of a number field $L$. A criterion for the class group of $L$ being generated by the classes of…

We prove formulas for the core of ideals that apply in arbitrary characteristic.

Given an ordinal delta <= lambda and a cardinal theta <= kappa, an ideal J on P_kappa(lambda) is said to be [delta]^{<theta}-normal if given B_e in J for e in P_theta(delta), the set of all a in P_kappa(lambda) such that a in B_e for some e…