Homological algebra and representation theory form a powerful confluence in modern mathematics. Homological algebra provides a framework for analysing algebraic structures via chain complexes, ...

We study the complexity of the problem to describe, up to unitary equivalence, representations of *-algebras by unbounded operators on a Hilbert space. A number of examples are developed in detail.

Quantum groups, as algebraic entities that extend classical group symmetries into the noncommutative domain, have increasingly become central to advances in both pure and applied mathematics. These ...

Current Projects • EXC 2044 - T04: Groups and actions The study of symmetry and space through the medium of groups and their actions has long been a central theme in modern mathematics, indeed one ...

Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the award ...

University of Chicago mathematicians Alexander Beilinson and Vladimir Drinfeld have been awarded the prestigious Wolf Prize for Mathematics “for their groundbreaking work in algebraic geometry, ...

My primary research interests are in algebra and combinatorics. In particular, I work within the realm of combinatorial representation theory, attempting to connect combinatorial objects (such as ...

Algebra teachers should show students both correctly and incorrectly solved problems and have students discuss them, according to a new algebra practice guide published by the U.S. Department of ...