### Members of the Lie unit

- Website: Link

## Prof. Domagoj Kovačević

#### Assistant Professor

**Position:**

- Assistant Professor at Faculty of Electrical Engineering and Computing

**Fields of interest:**

- Representation Theory
- Mathematical Physics

**Five selected publications:**

- D. Kovačević, S. Meljanac, A. Samsarov, Z. Škoda, Hermitian realizations of kappa-Minkowski spacetime, International journal of modern physics A 30 (2015) 1550019-1-1550019-26.
- T. Jurić, D. Kovačević, S. Meljanac, Kappa-deformed phase space, Hopf algebroid and twisting, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) (1815-0659) 10 (2014); 106-124.
- D. Kovačević, S. Meljanac, A. Pachol, R. Štrajn, Generalized Poincaré algebras, Hopf algebras and kappa-Minkowki spacetime, Physics Letters B 711 (2012) 122-127.
- D. Kovačević, S. Meljanac, Kappa-Minkowski spacetime, kappa-Poincaré Hopf algebra and realizations, J. Phys. A: Math. Theor. 45 (13) (2012) 135208.
- D. Kovačević, Real forms of dual pairs g2xh in g of type E6, E7 and E8, Journal of Lie theory 21(2) (2011) 417-426.

**The most important grants:**

- 2015- Member of the Scientific Center of Excellence for Quantum and Complex Systems – QuantiX
- 2009-2013 – Member of the project Quantum field theory, noncommutative spaces and symmetries funded by MZOS<

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**Bio:**

Domagoj Kovačević was born on January 14, 1968 in Požega, Croatia. He graduated from the High School in Zagreb. In 1986, he won bronze medal at the International Mathematical Olympiad in Poland. After the military service, he enrolled at the Department of Mathematics at the University of Zagreb. In 1993, he graduated and was enrolled as a PhD student at the University of Utah. His major interest during the graduate study was representation theory. In 2000, he came back and started to teach mathematics in XV. High School. In 2006, he defended his PhD thesis at the University of Utah. The thesis advisor was professor Gordan Savin. After that, Domagoj Kovačević became a Senior Instructor at the Faculty of Electrical Engineering and Computing at the University of Zagreb and started research collaboration with professor Stjepan Meljanac from Ruđer Bošković Intitute, where five papers were produced. In 2012, he became an Assistant Professor and started doing representation theory again. At the Faculty of Electrical Engineering and Computing he taught several undergraduate courses.

## Marijana Butorac

**Position:**

- Postdoctoral Research/Senior Assistant of Department of Mathematics at the University of Rijeka

**Fields of interest:**

- Infinite dimensional Lie algebras
- Vertex algebras
- Rogers-Ramanujan type identities

**Awards: ** –

**Five selected publications:**

- M. Butorac,
*Quasi-particle bases of principal subspaces of the affine Lie algebra of type*, accepted for publication in Glasnik Matematicki - M. Butorac,
*Quasi-particle bases of principal subspaces for the affine Lie algebras of types**and ,*Glasnik Matematicki, Vol. 51, No.1 (2016).

- Butorac,
*Combinatorial bases of principal subspaces for the affine Lie algebra of type*, J. Pure Appl. Algebra 218, No. 3 (2014).

**The most important grants (as PI):** –

**Bio:**

Marijana Butorac received a BSc degree in Mathematics and Physics from the Faculty of Humanities and Social Sciences, University of Rijeka (supervisor: Prof. Rajka Jurdana-Šepić) in 2005. In 2012 she defended her PhD thesis at the Faculty of Science, University of Zagreb (supervisor: Prof. Mirko Primc).

Since 2012 she works as a senior assistant at the Department of Mathematics, University of Rijeka. Prior to this, she worked as an assistant at the Department of Mathematics, University of Rijeka and at the Department of Mathematics, Faculty of Art and Sciences Rijeka and before that as a teacher of mathematics and physics at the “ Istituto professionale Buje” in Buje and at the elementary school “Gornja Vežica” in Rijeka.

She is a member of “Scientific Center of Excellence for Quantum and Complex Systems – QuantiX” and “Algebraic and combinatorial methods in vertex algebra theory” Croatian Science Foundation research project.

## Prof. Boris Širola

**Position:**

- Professor of mathematics at the Department of Mathematics, University of Zagreb

**Fields of interest:**

- Lie algebras and algebraic groups, and their representations; algebraic and geometric aspects
- Noncommutative algebra, algebraic number theory

**Five selected publications:**

- Širola,
*Distinguished nilpotent orbits, Kostant pairs and normalizers of Lie algebras*, J. Algebra 423 (2015), 636-682. - Širola,
*Compatible pairs of Borel subalgebras and shared orbit pairs*, J. Algebra 423 (2015), 726-766. - Širola,
*On Cartan subalgebras and Cartan subspaces of nonsymmetric pairs of Lie algebras,*Proc. Amer. Math. Soc. 141 (2013), 2233-2243. - Širola,
*On noncommutative Noetherian schemes*, J. Algebra 282 (2004), 667-698. - Širola,
*On supports and associated primes of modules over the enveloping algebras of nilpotent Lie algebras,*Trans. Amer. Math. Soc. 353 (2001), 2131-2170.

**The most important grants (as PI):**

- 2007-2013 Principal investigator at the project
*Enveloping algebras of Lie algebras and their modules*(no. 900-194134), funded by the Ministry of Science, Education and Sport in Croatia. - 2002-2006 Principal investigator at the project
*Restriction of representations of semisimple Lie groups and Lie algebras*(no. 0037121), funded by the Ministry of Science and Technology in Croatia. - 2000-2002 Principal investigator at the supporting project for young scientists
*Characteristic cycles and embedding of modules for enveloping algebras*(no. 037057), funded by the Ministry of Science and Technology in Croatia.

**Vita:**

Boris Širola earned a B.Sc. degree in mathematics at the Department of Mathematics, University of Zagreb, in 1988. He also earned a M.Sc. degree in 1992. and Ph.D. in 1996., at the same institution.

He held a position of a teaching assistant at the Department of Mathematics, University of Zagreb, since 1988. He received a permanent position of Assistant Professor in 2000., and was promoted to the rank of Associate Professor in 2005., and to the rank of Professor in 2012. An academic year 1998./99. he spent as a postdoc at the Massachusetts Institute of Technology, Cambridge, MA, USA. He has also been, as a visiting scholar, at the following institutions: Tata Institute of Fundamental Research, Mumbai (2002.); Mathematische Institut, Heinrich Heine Universitet, Dusseldorf (2005.); University of Utah, Salt Lake City (2010. i 2014.) His fields of interest are (noncommutative) algebra, group theory, number theory and mostly Lie theory; in particular, structure theory and representation theory of Lie algebras, some problems related to investigations of geometry of nilpotent orbits and flag varieties for reductive groups, and relationship with representation theory of algebraic groups. As an only author he published 21 scientific papers in recognized mathematical journals; some of them in leading journals specialized for algebra.

At the undergraduate study he held several courses (e.g., Algebraic structures, Theory of analytic functions). At the graduate study he created and held 4 two-semester courses (Lie algebras and representation theory, Commutative algebra, Riemann Zeta function and Introduction to the theory of analytic functions of several complex variables). He is a cofounder and coleader of the Seminar for Algebra at the University of Zagreb.