Gateva-Ivanova, Tatiana

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Gateva-Ivanova, Tatiana

Email Degree Ph.D., Mathematics, Algebra, Moscow State University, Russia

Courses

  • Elementary Linear Algebra and Analytical Geometry, MAT 1005
  • Introduction to Abstract Algebra, MAT 2005
  • Advanced Linear Algebra, MAT 2025
  • Calculus III - Multivariate Calculus and Geometry, MAT 2012
  • Introduction to Lie Algebras
  • Fields and Galois Theory
  • Ideals, Varieties and Algorithms

Research Interests

  • Non-commutative algebra and applications for quantum groups
  • Representation theory, Non-commutative algebraic geometry
  • Symbolic computation, Combinatorial methods in noncommutative algebra

Education

Ph.D., Mathematics, Algebra, Moscow State University, Russia
M.A., Mathematics, Algebra, Sofia University, Bulgaria
Fulbright Research Scholar at Massachusetts Institute of Technology (MIT), USA, 1994-95

Graduate courses taught in Research Universities
Combinatorial Methods in Non-commutative Algebra; Algebra;  Set-Theoretic solutions of the Yang-Baxter equation and related algebraic objects.

Topics of Studies

  • Set-theoretic solutions of the Yang-Baxter equation and related algebraic objects;
  • Braided groups;
  • Noncommutative algebraic geometry – Artin-Schelter regular algebras;
  • Quadratic Algebras;
  • Lyndon Words, Associative algebras and Lie Algebras defined by Lyndon words;
  • Combinatorial methods in noncommutative algebra: the study of concrete algebras, monoids, and groups presented via generators and relations;
  • Symbolic computation, Rewriting systems. Noncommutative Groebner-Shirshov bases (Diamond Lemma)

Selected Publications

  • Tatiana Gateva-Ivanova, Veronese subalgebras and Veronese morphisms for a class of Yang–Baxter algebras. J. Noncommut. Geom. (2025), published online first  DOI 10.4171/JNCG/626
  • Gateva-Ivanova, T., & Majid, S. (2024). Quadratic algebras and idempotent braided sets [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2409.02939
  • Gateva-Ivanova, T. (2023). Segre products and Segre morphisms in a class of Yang–Baxter algebras. Letters in Mathematical Physics, 113. https://doi.org/10.1007/s11005-023-01657-z
  • Gateva-Ivanova, T. (2022). Algebras defined by Lyndon words and Artin-Schelter regularity. Transactions of the American Mathematical Society, Series B, 9, 648–699. https://doi.org/10.1090/btran/89
  • Arici, F., Galuppi, F., & Gateva-Ivanova, T. (2022). Veronese and Segre morphisms between non-commutative projective spaces. European Journal of Mathematics, 8, 235-273. https://doi.org/10.1007/s40879-022-00547-3

Bibliography