N. Ngo

activity

20102026

r

-tuples over Lie algebras

14 citations · 54 across the 12 of their papers we have counts for

collaborators

14 papers

math.GR2026

Linear Bounds for Cohomology of Algebraic Groups

Christopher P. Bendel, Nham Ngo

In this note, we establish an explicit upper bound for the dimension of the rational cohomology for a simple algebraic group over an algebraically closed field of prime characteris…

math.RT2023

Restricted Partitions and $S L_{2}$ Cohomology

Steven Benzel, Scott Conner, Nham Ngo +1

The aim of this paper is twofold. First, we study the number of partitions of a positive integer $m$ into at most $n$ parts in a given set $A$ . We prove that such a number is bound…

math.RT2021★ 1 cited

Commuting Varieties and Cohomological Complexity

Nham V. Ngo, Paul D. Levy, Klemen Šivic

In this paper we determine, for all $r$ sufficiently large, the irreducible component(s) of maximal dimension of the variety of commuting $r$ -tuples of nilpotent elements of $\math…

math.RT2015

Cohomology of $S L_{2}$ and related structures

Klaus Lux, Nham V. Ngo, Yichao Zhang

Let $S L_{2}$ be the rank one simple algebraic group defined over an algebraically closed field $k$ of characteristic $p > 0$ . The paper presents a new method for computing the dimensio…

math.RT2014

On nilpotent commuting varieties and cohomology of Frobenius kernels

Nham V. Ngo

The paper studies the dimensions of irreducible components of commuting varieties of (restricted) nilpotent $r$ -tuples in a classical Lie algebra $g$ defined over an alg…

math.RT2013

Rational singularities of $G$ -saturation

Nham V. Ngo

Let $G$ be a semisimple algebraic group defined over an algebraically closed field of characteristic 0 and $P$ be a parabolic subgroup of $G$ . Let $M$ be a $P$ -module and $V$ be a…

math.RT2013★ 3 cited

Reducibility of nilpotent commuting varieties

Robert M. Guralnick, Nham V. Ngo

Let $N_{n}$ be the set of nilpotent $n$ by $n$ matrices over an algebraically closed field $k$ . For each $r \geq 2$ , let $C_{r} (N_{n})$ be the variety consisting of all pairwise commutin…

math.AG2013

On varieties of commuting nilpotent matrices

Nham V. Ngo, Klemen Šivic

Let $N (d, n)$ be the variety of all $d$ -tuples of commuting nilpotent $n \times n$ matrices. It is well-known that $N (d, n)$ is irreducible if $d = 2$ , if $n \leq 3$ or if $d = 3$ and $n = 4$ …

math.RT2013

Mixed Commuting Varieties over simple Lie algebras

Nham V. Ngo

Let $g$ be a simple Lie algebra defined over an algebraically closed field $k$ of characteristic $p$ . Fix an integer $r > 1$ and suppose that $V_{1}, \dots, V_{r}$ are irreduci…

math.RT2012★ 10 cited

Cohomology for Frobenius kernels of $S L_{2}$

Nham V. Ngo

Let $(S L_{2})_{r}$ be the $r$ -th Frobenius kernels of the group scheme $S L_{2}$ defined over an algebraically field of characteristic $p > 2$ . In this paper we give for $r \geq 1$ a complete…

math.RT2012★ 14 cited

Commuting varieties of $r$ -tuples over Lie algebras

Nham V. Ngo

Let $G$ be a simple algebraic group defined over an algebraically closed field $k$ of characteristic $p$ and let $\g$ be the Lie algebra of $G$ . It is well known that for $p$ large…

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.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…

Linear Bounds for Cohomology of Algebraic Groups

Restricted Partitions and SL2​ Cohomology

Commuting Varieties and Cohomological Complexity

Cohomology of SL2​ and related structures

On nilpotent commuting varieties and cohomology of Frobenius kernels

Rational singularities of G-saturation

Reducibility of nilpotent commuting varieties

On varieties of commuting nilpotent matrices

Mixed Commuting Varieties over simple Lie algebras

Cohomology for Frobenius kernels of SL2​

Commuting varieties of r-tuples over Lie algebras

Second cohomology for finite groups of Lie type

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

Cohomology for infinitesimal unipotent algebraic and quantum groups

Restricted Partitions and $S L_{2}$ Cohomology

Cohomology of $S L_{2}$ and related structures

Rational singularities of $G$ -saturation

Cohomology for Frobenius kernels of $S L_{2}$

Commuting varieties of $r$ -tuples over Lie algebras