C. Drupieski

activity

20092025

most citedCohomological finite-generation for finite supergroup schemes

25 citations · 149 across the 24 of their papers we have counts for

collaborators

24 papers

math.RT2025

Lie Superalgebras Generated by Reflections in Weyl Groups of Classical Type

Christopher M. Drupieski, Jonathan R. Kujawa

We consider the finite Weyl groups of classical type -- $W (A_{r})$ for $r \geq 1$ , $W (B_{r}) = W (C_{r})$ for $r \geq 2$ , and $W (D_{r})$ for $r \geq 4$ -- as supergroups in which th…

math.RT2025

Lie algebras generated by reflections in types BCD

Christopher M. Drupieski, Jonathan R. Kujawa

We consider the group algebra over the field of complex numbers of the Weyl group of type B (the hyperoctahedral group, or the group of signed permutations) and of the Weyl group o…

math.RT2023

The Lie superalgebra of transpositions

Christopher M. Drupieski, Jonathan R. Kujawa

We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of t…

math.RT2022

A survey of support theories for Lie superalgebras and finite supergroup schemes

Christopher M. Drupieski, Jonathan R. Kujawa

We survey the current state of various support variety theories for Lie superalgebras and finite supergroup schemes. We pay particular attention to the theory in characteristic zer…

math.RT2022

Support varieties for Lie superalgebras in characteristic 2

Christopher M. Drupieski, Jonathan R. Kujawa

This paper investigates cohomology and support varieties for Lie superalgebras and restricted Lie superalgebras over a field of characteristic 2. The existence of an underlying ord…

math.RT2021

Superized Troesch complexes and cohomology for strict polynomial superfunctors

Christopher M. Drupieski, Jonathan R. Kujawa

We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Fro…

math.RT2019★ 5 cited

Support varieties and modules of finite projective dimension for modular Lie superalgebras (with an appendix on homological dimensions over Noether Algebras by Luchezar L. Avramov and Srikanth B. Iyengar)

Christopher M. Drupieski, Jonathan R. Kujawa

We investigate cohomological support varieties for finite-dimensional Lie superalgebras defined over fields of odd characteristic. Verifying a conjecture from our previous work, we…

math.RT2018★ 7 cited

Support schemes for infinitesimal unipotent supergroups

Christopher M. Drupieski, Jonathan R. Kujawa

We investigate support schemes for infinitesimal unipotent supergroups and their representations. Our main results provide a non-cohomological description of these schemes which ge…

math.RT2017★ 4 cited

On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

Christopher M. Drupieski, Jonathan R. Kujawa

We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$ , then the cohomological spectrum $∣ G ∣$ of $G$ is naturally homeomorphic to the variety $\mat…

math.RT2017★ 9 cited

Graded analogues of one-parameter subgroups and applications to the cohomology of $G L_{m ∣ n (r)}$

Christopher M. Drupieski, Jonathan R. Kujawa

We introduce a family $M_{r; f, η}$ of infinitesimal supergroup schemes, which we call multiparameter supergroups, that generalize the infinitesimal Frobenius kernels $\math…

math.RT2016

Corrigendum to "On injective modules and support varieties for the small quantum group"

Christopher M. Drupieski

The proof of Theorem 5.12 in [C.M. Drupieski, On injective modules and support varieties for the small quantum group, Int. Math. Res. Not. 2011 (2011), 2263-2294] does not make sen…

math.RT2016★ 13 cited

On support varieties for Lie superalgebras and finite supergroup schemes

Christopher M. Drupieski, Jonathan R. Kujawa

We study the spectrum of the cohomology rings of cocommutative Hopf superalgebras, restricted and non-restricted Lie superalgebras, and finite supergroup schemes. We also investiga…

math.RT2015★ 2 cited

Extensions for Generalized Current Algebras

Brian D. Boe, Christopher M. Drupieski, Tiago R. Macedo +1

Given a complex semisimple Lie algebra $g$ and a commutative $C$ -algebra $A$ , let $g [A] = g \otimes A$ be the corresponding generalize…

math.RT2014★ 25 cited

Cohomological finite-generation for finite supergroup schemes

Christopher M. Drupieski

In this paper we compute extension groups in the category of strict polynomial superfunctors and thereby exhibit certain "universal extension classes" for the general linear superg…

math.RT2013

Universal extension classes for $G L_{2}$

Christopher M. Drupieski

In this note we give a new existence proof for the universal extension classes for $G L_{2}$ previously constructed by Friedlander and Suslin via the theory of strict polynomial funct…

math.RT2013★ 4 cited

Bounding the dimensions of rational cohomology groups

Christopher P. Bendel, Brian D. Boe, Christopher M. Drupieski +4

Let $k$ be an algebraically closed field of characteristic $p > 0$ , and let $G$ be a simple simply-connected algebraic group over $k$ that is defined and split over the prime field…

math.RT2013★ 15 cited

Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

Christopher M. Drupieski

We prove that the cohomology ring of a finite-dimensional restricted Lie superalgebra over a field of characteristic $p > 2$ is a finitely-generated algebra. Our proof makes essent…

math.RT2011★ 9 cited

Second cohomology for finite groups of Lie type

Brian D. Boe, Brian Bonsignore, Theresa Brons +13

Let $G$ be a simple, simply-connected algebraic group defined over $F_{p}$ . Given a power $q = p^{r}$ of $p$ , let $G (F_{q}) \subset G$ be the subgroup of $F_{q}$ …

math.QA2010

Cohomology rings for quantized enveloping algebras

Christopher M. Drupieski

We compute the structure of the cohomology ring for the quantized enveloping algebra (quantum group) $U_{q}$ associated to a finite-dimensional simple complex Lie algebra $\mathfrak{…

math.GR2010★ 12 cited

First cohomology for finite groups of Lie type: simple modules with small dominant weights

Brian D. Boe, Adrian M. Brunyate, Jon F. Carlson +12

Let $k$ be an algebraically closed field of characteristic $p > 0$ , and let $G$ be a simple, simply connected algebraic group defined over $F_{p}$ . Given $r \geq 1$ , set $q=…

math.RT2010★ 5 cited

Cohomology for infinitesimal unipotent algebraic and quantum groups

Christopher M. Drupieski, Daniel K. Nakano, Nham V. Ngo

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple…

math.RT2010★ 19 cited

Representations and cohomology for Frobenius-Lusztig kernels

Christopher M. Drupieski

Let $U_{ζ}$ be the quantum group (Lusztig form) associated to the simple Lie algebra $g$ , with parameter $ζ$ specialized to an $ℓ$ -th root of unity in a field of charac…

math.RT2009★ 4 cited

On injective modules and support varieties for the small quantum group

Christopher M. Drupieski

Let $u_{ζ} (g)$ denote the small quantum group associated to the simple complex Lie algebra $g$ , with parameter $q$ specialized to a primitive $ℓ$ -th root of unity $ζ$ in the field…

math.GR2009★ 16 cited

Differentiating the Weyl generic dimension formula and support varieties for quantum groups

Christopher M. Drupieski, Daniel K. Nakano, Brian J. Parshall

The authors compute the support varieties of all irreducible modules for the small quantum group $u_{ζ} (g)$ , where $g$ is a simple complex Lie algebra, and $ζ$ …

Lie Superalgebras Generated by Reflections in Weyl Groups of Classical Type

Lie algebras generated by reflections in types BCD

The Lie superalgebra of transpositions

A survey of support theories for Lie superalgebras and finite supergroup schemes

Support varieties for Lie superalgebras in characteristic 2

Superized Troesch complexes and cohomology for strict polynomial superfunctors

Support varieties and modules of finite projective dimension for modular Lie superalgebras (with an appendix on homological dimensions over Noether Algebras by Luchezar L. Avramov and Srikanth B. Iyengar)

Support schemes for infinitesimal unipotent supergroups

On the cohomological spectrum and support varieties for infinitesimal unipotent supergroup schemes

Graded analogues of one-parameter subgroups and applications to the cohomology of GLm∣n(r)​

Corrigendum to "On injective modules and support varieties for the small quantum group"

On support varieties for Lie superalgebras and finite supergroup schemes

Extensions for Generalized Current Algebras

Cohomological finite-generation for finite supergroup schemes

Universal extension classes for GL2​

Bounding the dimensions of rational cohomology groups

Cohomological finite generation for restricted Lie superalgebras and finite supergroup schemes

Second cohomology for finite groups of Lie type

Cohomology rings for quantized enveloping algebras

First cohomology for finite groups of Lie type: simple modules with small dominant weights

Cohomology for infinitesimal unipotent algebraic and quantum groups

Representations and cohomology for Frobenius-Lusztig kernels

On injective modules and support varieties for the small quantum group

Differentiating the Weyl generic dimension formula and support varieties for quantum groups

Graded analogues of one-parameter subgroups and applications to the cohomology of $G L_{m ∣ n (r)}$

Universal extension classes for $G L_{2}$