Professor Roozbeh Hazrat
Professor,
Mathematics
Biography
Roozbeh Hazrat obtained his PhD in Pure Mathematics from the University of Bielefeld, Germany in 2002. He did research at the Australian National University, Max Planck Institute in Bonn and the City University of New York. He was a Reader (Associate Professor) in Pure Mathematics at Queen's University Belfast, United Kingdom where he worked for 8 years, before moving to University of Western Sydney in December 2011. In 2015 he was awarded a one year Fellowship for Experienced Researchers by Germany's Alexander von Humboldt Foundation.
This information has been contributed by Professor Hazrat.
Qualifications
 PhD Bielefeld University
Interests
 Algebraic Ktheory and Noncommutative algebras
Organisational Unit (School / Division)
 Mathematics
Contact
Email:  R.Hazrat@westernsydney.edu.au 

Phone:  (02) 9685 9054 
Mobile:  
Location:  EN.1.41 Parramatta 
Website: 
PLEASE NOTE: obtaining information from this Directory must be for the legitimate purposes of doing business with and within Western Sydney University, and must not be used for unsolicited bulk emailing (spamming) or similar purposes.
Teaching
Previous Teaching Areas
 301031 Computer Algebra, 2018
Publications
Books
 Hazrat, R. (2016), 'Graded Rings and Graded Grothendieck Groups', : Cambridge University Press 9781316619582.
 Hazrat, R. (2015), 'Mathematica?: A Problemcentered Approach', : Springer 9783319275840.
 Hazrat, R. (2010), 'Mathematica: A ProblemCentered Approach', : SpringerVerlag 9781849962506.
Journal Articles
 Clark, L., Hazrat, R. and Rigby, S. (2019), 'Strongly graded groupoids and strongly graded Steinberg algebras', Journal of Algebra, vol 530 , pp 34  68.
 Ambily, A., Hazrat, R. and Li, H. (2019), '[In Press] Simple flat Leavitt path algebras are von Neumann regular', Communications in Algebra, .
 Hazrat, R. and Vas, L. (2018), 'Baer and Baer *ring characterizations of Leavitt path algebras', Journal of Pure and Applied Algebra, vol 222, no 1 , pp 39  60.
 Hazrat, R., Rangaswamy, K. and Srivastava, A. (2018), 'Leavitt path algebras : graded directfiniteness and graded Sinjective simple modules', Journal of Algebra, vol 503 , pp 299  328.
 Hazrat, R. and Li, H. (2018), 'Graded Steinberg algebras and partial actions', Journal of Pure and Applied Algebra, vol 222, no 12 , pp 3946  3967.
 Ara, P., Hazrat, R., Li, H. and Sims, A. (2018), 'Graded Steinberg algebras and their representations', Algebra and Number Theory, vol 12, no 1 , pp 131  172.
 Hazrat, R. and Vas, L. (2018), 'Ktheory classification of graded ultramatricial algebras with involution', Forum Mathematicum, vol 31, no 2 , pp 419  463.
 Hazrat, R., Vavilov, N. and Zhang, Z. (2017), 'The commutators of classical groups', Journal of Mathematical Sciences, vol 222, no 4 , pp 466  515.
 Hazrat, R. and Preusser, R. (2017), 'Applications of normal forms for weighted Leavitt path algebras : simple rings and domains', Algebras and Representation Theory, vol 20, no 5 , pp 1061  1083.
 Hazrat, R., Vavilov, N. and Zhang, Z. (2017), 'Multiple commutator formulas for unitary groups', Israel Journal of Mathematics, vol 219, no 1 , pp 287  330.
 Ara, P., Bosa, J., Hazrat, R. and Sims, A. (2017), 'Reconstruction of graded groupoids from graded Steinberg algebras', Forum Mathematicum, vol 29, no 5 , pp 1023  1037.
 Hazrat, R. and Rangaswamy, K. (2016), 'On graded irreducible representations of Leavitt path algebras', Journal of Algebra, vol 450 , pp 458  486.
 Hazrat, R., Vavilov, N. and Zhang, Z. (2016), 'Generation of relative commutator subgroups in Chevalley groups', Proceedings of the Edinburgh Mathematical Society, vol 59, no 2 , pp 393  410.
 Hazrat, R. and Huang, J. (2016), 'Recollements, sinks elimination, and Leavitt path algebras', Archiv der Mathematik, vol 107, no 6 , pp 589  594.
 Hazrat, R. (2014), 'Leavitt path algebras are graded von Neumann regular rings', Journal of Algebra, vol 401 , pp 220  233.
 Hazrat, R., MahdaviHezavehi, M. and Motiee, M. (2014), 'Multiplicative groups of division rings', Mathematical Proceedings of Royal Irish Academy, vol 114, no 1 , pp 37  114.
 Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2014), 'The yoga of commutators : further applications', Journal of Mathematical Sciences, vol 200, no 6 , pp 742  768.
 Hazrat, R. (2013), 'The graded structure of Leavitt path algebras', Israel Journal of Mathematics, vol 195, no 2 , pp 833  895.
 Hazrat, R. and Zhang, Z. (2013), 'Multiple commutator formulas', Israel Journal of Mathematics, vol 195, no 1 , pp 481  505.
 Hazrat, R. (2013), 'The graded Grothendieck group and the classication of Leavitt path algebras', Mathematische Annalen, vol 355, no 1 , pp 273  325.
 Hazrat, R. and Hoobler, R. (2013), 'Ktheory of Azumaya algebras over schemes', Communications in Algebra, vol 41, no 4 , pp 1268  1277.
 Hazrat, R. (2013), 'A note on the isomorphism conjectures for Leavitt path algebras', Journal of Algebra, vol 375 , pp 33  40.
 Hazrat, R., Vavilov, N. and Zhang, Z. (2013), 'Relative commutator calculus in Chevalley groups', Journal of Algebra, vol 385 , pp 262  293.
 Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2013), 'Commutator width in Chevalley groups', Note di Matematica, vol 33, no 1 , pp 139  170.
 Hazrat, R. (2013), 'The dynamics of Leavitt path algebras', Journal of Algebra, vol 384 , pp 242  266.
 Hazrat, R. and Huttemann, T. (2013), 'On Quillen's calculation of graded Ktheory', Journal of Homotopy and Related Structures, vol 8, no 2 , pp 231  238.
 Hazrat, R. (2012), 'Stability of unitary SK1 of Azumaya algebras', Archiv der Mathematik, vol 98, no 1 , pp 19  23.
 Hazrat, R. and Wadsworth, A. (2012), 'Homogeneous SK1 of simple graded algebras', New York Journal of Mathematics, vol 18 , pp 315  336.
 Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2011), 'The yoga of commutators', Journal of Mathematical Sciences, vol 179, no 6 , pp 662  678.
 Hazrat, R., Zhang, Z. and Vavilov, N. (2011), 'Relative unitary commutator calculus, and applications', Journal of Algebra, vol 343, no 1 , pp 107  137.
 Hazrat, R. and Wadsworth, A. (2011), 'Unitary and graded SK1 of division algebras', London Mathematical Society. Proceedings, vol 103, no 3 , pp 508  534.
 Hazrat, R. and Wadsworth, A. (2011), 'SK1 of graded division algebras', Israel Journal of Mathematics, vol 183, no 1 , pp 117  163.
 Hazrat, R. and Zhang, Z. (2011), 'Generalized commutator formulas', Communications in Algebra, vol 39, no 4 , pp 1441  14564.
 Hazrat, R. (2010), 'SK1 of Azumaya algebras over Hensel pairs', Mathematische Zeitschrift, vol 264, no 2 , pp 295  299.
 Hazrat, R. and Millar, J. (2010), 'On graded central simple algebras', Homotopy and related structures, vol 5, no 1 , pp 113  124.
 Hazrat, R., Petrov, V. and Vavilov, N. (2010), 'Relative subgroups in Cheavelly groups', Journal of KTheory, vol 5, no 3 , pp 603  618.
 Hazrat, R. and Millar, J. (2010), 'A note on Ktheory of Azumaya algebras', Communications in Algebra, vol 38, no 3 , pp 919  926.
 Hazrat, R. and Wadsworth, A. (2009), 'On maximal subgroups of the multiplicative group of a division algebra', Journal of Algebra, vol 322, no 7 , pp 2528  2543.
 Hazrat, R. and Vavilov, N. (2009), 'Bak's work on Ktheory of rings', Journal of KTheory, vol 4, no 1 , pp 1  65.
 Hazrat, R., Bak, A. and Vavilov, N. (2009), 'Localizationcompletion strikes again : relative K1 is nilpotent by abelian', Journal of Pure and Applied Algebra, vol 213, no 6 , pp 1075  1085.
 Hazrat, R. (2008), 'On the first Galois cohomology group of the algebraic group SL1(D)', Communications in Algebra, vol 36, no 2 , pp 381  387.
 Hazrat, R. and Wadsworth, A. (2007), 'Nontriviality of certain quotients of K1 groups of division algebras', Journal of Algebra, vol 312, no 1 , pp 354  361.
 Hazrat, R. (2006), 'Reduced Ktheory for Azumaya algebras', Journal of Algebra, vol 305, no 2 , pp 687  703.
 Hazrat, R. and Wilson, R. (2006), 'A decomposition theorem for CK1 of central simple algebras', Communications in Algebra, vol 34, no 12 , pp 4573  4578.
 Hazrat, R. and Vishne, U. (2005), 'Triviality of the functor Coker(K1(F) ! K1(D)) for division algebras', Communications in Algebra, vol 33, no 5 , pp 1427  1435.
 Hazrat, R. and Vavilov, N. (2003), 'K1 of Chevalley groups are nilpotent', Journal of Pure and Appl. Algebra, vol 179, no 12 , pp 99  116.
 Hazrat, R. (2002), 'On central series of the multiplicative group of division rings', Algebra Colloquium, vol 9, no 1 , pp 99  106.
 Hazrat, R. (2002), 'Wedderburn's factorization theorem, Application to reduced Ktheory', Proceedings of the American Mathematical Society, vol 130, no 2 , pp 311  314.
 Hazrat, R. (2002), 'Dimension theory and nonstable K1 of quadratic modules', KTheory, vol 27, no 4 , pp 293  328.
 Hazrat, R. (2001), 'SK1like functors for division algebras', Journal of Algebra, vol 239, no 2 , pp 573  588.
Current Projects
Title:  Graded Ktheory as invariants for path algebras 

Funder: 

Western Researchers:  Roozbeh Hazrat 
Years:  20160630  20190731 
ID:  P00022561 
Previous Projects
Title:  RBA Mathematica Training  Stage 2 Software Coding, Implementation & Training + 2017 Mathematic Training Courses 

Funder: 

Western Researchers:  
Years:  20140310  20150113 
ID:  P00024306 
Title:  Groupoids as bridges between algebra and analysis [via UoW] 
Funder: 

Western Researchers:  Roozbeh Hazrat 
Years:  20150218  20171231 
ID:  P00022485 