We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant 4-ended tangles which the author introduced in \[J. Topol. 13 (2020)]. In particular, we give an almost complete answer to geography problem for components modules tangles. As main application, show that Conway mutation preserves hat flavour relatively $\delta$-graded theory links.

The main result of this paper is that over a noncommutative Koszul algebra, high truncations of finitely generated graded modules have linear free resolutions.

We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated in [FS]. We establish a linear bound on the degree of tensor field modules appearing in the Jordan-Hölder series of each graded component, which is conjecturally tight. We also bound the leading coefficient of the Hilbert polynomial of each graded...

We prove asymptotic normality of the distributions defined by q-supernomials, which implies asymptotic normality of the distributions given by the central string functions and the basic specialization of fusion modules of the current algebra of sl2. The limit is taken over linearly scaled fusion powers of a fixed collection of irreducible representations. This includes as special instances all ...

Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived cat...

The cohomology groups of the configuration space of ordered k–tuples of distinct points in Euclidean space give natural modules over the group ring of the symmetric group. On the other hand, these modules are basic building blocks for certain free graded Lie algebras. Thus we consider the representation theory of these modules in some detail. These results overlap with some recent results of Er...

With the $\Omega$-operators for Virasoro algebra \cite{BF} and super in \cite{CL, CLL}, we get Ovsienko-Roger superalgebras this paper then use it to classify all simple cuspidal modules $\bZ$-graded $\frac12\bZ$-graded superalgebras. By result, can easily Harish-Chandra over some related Lie superalgebras, including $N=1$ BMS$_3$ algebra, $W(2,2)$, etc.

It gives a class of p-Borel principal ideals of a polynomial algebra over a field K for which the graded Betti numbers do not depend on the characteristic of K and the Koszul homology modules have monomial cyclic basis. Also it shows that all principal p-Borel ideals have binomial cycle basis on Koszul homology modules.

We compute the Grothendieck and Picard groups of a smooth toric DM stack by using a suitable category of graded modules over a polynomial ring.

We compute the Grothendieck and Picard groups of a complete smooth toric DM stack by using a suitable category of graded modules over a polynomial ring.