Tenured Professor of Mathematics (Professor Associado IV) · UFSCar
Waldeck Schützer
Algebra, mathematical art and photography
0000-0001-9098-2519Currículo LattesarXivGoogle ScholarGoogle Scholar IDKELzmVsAAAAJMathSciNetMathSciNet author ID995806zbMATH OpenResearchGateGitHubwaldeck@ufscar.brBiography
I teach and do research in the Department of Mathematics at the Universidade Federal de São Carlos (UFSCar), in São Carlos, Brazil. My work is in algebra, mostly on the structure and symmetries of associative algebras: algebras graded by groups and their generalizations (H-comodule algebras), incidence algebras, and polynomial identities as a way to tell algebras apart. I like finding explicit descriptions, such as parametrizations, normal forms and criteria for when two algebras are the same, and principles for reducing a problem to simpler pieces and gluing them back together, in finite and infinite dimensions, including over indecomposable commutative rings. I also work in the representation theory of algebras and groups, and I enjoy its combinatorial and computational side.
- Polynomial identities of matrix algebras
- H-comodule algebras, group gradings and graded identities
- Incidence algebras and their generalizations
- Hopf algebras and H-identities
- Representation theory: characters of Lie algebras and groups
- Algebraic combinatorics: Jack polynomials and Pieri rules
- Representations of the symmetric group and cocharacters
- Computer-assisted algebra with certified results
- Mathematical art, creative coding and photography
Recent work
- preprintA classification of group gradings on incidence algebras over commutative rings (2026)Earlier working title: Primitive idempotents and gradings of incidence algebras over commutative rings.
- preprintAtomic decompositions of Lie characters and the dominant weight poset (2026)Earlier working title: The atomic decomposition of characters of complex semisimple finite-dimensional Lie algebras.
- preprintGraded bimodules over split group algebras: stabilizers and Peirce decompositions (2026)
- preprintDegree-one Pieri rule for non-symmetric Jack polynomials (2026)
Products
Matrix algebras identities database
Browse the polynomial identities, central polynomials, weak identities and A-identities of the matrix algebras \(M_r(F)\) in low degree: Specht-module multiplicities with certified lower and upper bounds, codimension sequences, and searchable tables.
artMathematical animations
Short looping animations of mathematical objects, posted as @infinitymathart.
softwarexsvfduino
Turns an Arduino (the Blue Pill, STM32F103) into an XSVF player that programs CPLDs and FPGAs over JTAG. Tested on Xilinx XC2C64A and XC9572XL and Altera MAX II EPM240T. GPL-3.0.
photoUFSCar: campo in natura
Photo album of the São Carlos campus of UFSCar and its natural surroundings.
LaTeX tools: LatexRender-ng and a UFSCar LaTeX style file
LatexRender-ng renders LaTeX formulas for web pages; the style file was written with M. J. Soares for the UAB-UFSCar course collection.
NutMail
An e-mail classification and routing system.
Linear algebra video lessons
Short videos on Gauss-Jordan elimination, linear combinations, linear dependence, general solution of linear systems, inverse matrices, and determinants by row reduction and by cofactors.