IPM Positions

Professor, School of Mathematics - Isfahan Branch (2016 - Present )

Past IPM Positions

Senior Associate Researcher, School of Mathematics (2014 - 2016) (From September 23 in IPM-Isfahan Branch till September 21, 2016 ) Senior Associate Researcher, School of Mathematics (2010 - 2013) Associate Researcher (non-resident), School of Mathematics (2006 - 2007) Associate Researcher (non-resident), School of Mathematics (2005 - 2006) Associate Researcher (non-resident), School of Mathematics (2003 - 2004) Associate Researcher (non-resident), School of Mathematics (1988 - 2003)

Non IPM Affiliations

Professor of University of Isfahan

Research Activities

There are two notions of extended affine root systems in the literature which both are introduced axiomatically. One extended affine root system (called SEARS for short) which is introduced in 1985 by K. Saito, consists of only non isotropic roots, while the other extended affine root system (called EARS for short) which is introduced in 1997 by B. Allison, S. Azam, S. Berman, Y. Gao and A. Pianzola, contains certain isotropic roots too. In 2002, the relation between SEARS and EARS is clarified. In fact it is known that there is a one to one correspondence between (reduced) SEAR and EARS. In 1997, the BC-type EARS of nullity less than or equal ? 3 are classified, so the classification problem for BC-type SEARS of nullity less than or equal ? 3 is completely solved. Here two more natural questions arise. Namely, what is the relation between SEARS (not necessarily reduced) and EARS? and what is the classification list for BC-type SEARS (not necessarily reduced) of nullity less than or equal 3? The goal of this project is to investigate the above two questions.

Related Papers

1.	S. Azam and G. Behboodi Derivations of extended multi-loop algebras J. Lie Theory 29 (2019), 247-262  [abstract]

2.	S. Azam and A. Farahmand Parsa Groups of extended affine Lie type Publ. RIMS, Kyoto Univ. 55 (2019), 627-649  [abstract]

3.	S. Azam A new characterization of Kac-Moody-Malcev superalgebras J. Algebra Appl. 16 (2017), # 15 Pages  [abstract]

4.	S. Azam, G. Behboodi and M. Yousofzadeh Direct unions of Lie Tori (realization of locally extended affine Lie algebras) Comm. Algebra 44 (2016), 5309-5341  [abstract]

5.	S. Azam (Joint with G. Behboodi and M. Yousofzadeh) Direct unions of Lie tori (Realization of locally extended affine Lie algebras) Comm. Algebra 44 (2016), 5309-5341  [abstract]

6.	S. Azam and M. Yousofzadeh (Joint with H. Yamane) Classification of finite-dimensional irreducible representations of generalized quantum groups via Weyl groupoids Publ. RIMS, Kyoto Univ. 51 (2015), 59-130  [abstract]

7.	S. Azam and M. Yousofzadeh (Joint with Y. Yoshi) Jordan tori for a torsion free abelian group Front. Math. China 10 (2015), 477-509  [abstract]

8.	S. Azam (Joint with K.-H. Neeb) Finite dimensional compact and unitary Lie superalgebras J. Pure Appl. Algebra 219 (2015), 4422-4440  [abstract]

9.	S. Azam (Joint with M. Nikouei) A length function for Weyl groups of extended affine root systems of type A1 Algebra Colloq. (Accepted) [abstract]

10.	S. Azam (Joint with M. Nikouei) Weyl groups associated with affine reflection systems of type A1 (Coxeter type defining relations) Publ. RIMS, Kyoto Univ. 49 (2013), 123-153  [abstract]

11.	S. Azam and M. Yousofzadeh (Joint with S. Reza Hosseini) Extended affinization of invariant affine reflection algebras Osaka J. Math. 50 (2013), 1039-1072  [abstract]

12.	S. Azam and M. Yousofzadeh (Joint with H. Yamane) Reflectable bases for affine reflection systems J. Algebra 371 (2012), 63-93  [abstract]

13.	S. Azam and M. Yousofzadeh Root systems arising from automorphisms J. Algebra Appl. 11 (2012), #P29  [abstract]

14.	S. Azam (Joint with H. Yamane and M. Yousofzadeh) Exposition on affine and elliptic root systems and elliptic Lie algebras ( In: The Proceedings of New developments in group representation theory and noncommutative harmonic analysis) [abstract]

15.	S. Azam (Joint with V. Shahsanaei) Extended affine Weyle group: Presentation by conjugation via integral collection Comm. Algebra 39 (2011), 730-749  [abstract]

16.	S. Azam (Joint with H. Yamane and M. Yousofzadeh) A finite presentation of universal coverings of Lie tori Publ. RIMS, Kyoto Univ. 46 (2010), 507-548  [abstract]

17.	S. Azam (Joint with V. Shahsanaei) On the presentations of extended affine Weyl groups Publ. RIMS, Kyoto Univ. 44 (2008), 131-161  [abstract]

18.	S. Azam Derivations of tensor product algebras Comm. Algebra 36 (2008), 905-927  [abstract]

19.	S. Azam (Joint with V. Shahsanaei) Simply laced extended affine Weyl groups (a finite presentation) Publ. RIMS, Kyoto Univ. 43 (2007), 403-424  [abstract]

20.	S. Azam Derivations of multi-loop algebras Forum Math. 19 (2007), 1029–1045  [abstract]

21.	S. Azam, S. Berman and M. Yousofzadeh Fixed point subalgebras of extended affine lie algebras J. Algebra 287 (2005), 351-380  [abstract]

22.	S. Azam, V. Khalili and M. Yousofzadeh Extended affine root systems of type BC J. Lie Theory 15 (2005), 145-181  [abstract]

23.	S. Azam Nonreduced extended affine Weyl groups J. Algebra 269 (2003), 508-527  [abstract]

24.	S. Azam Extended affine root systems J. Lie Theory 12 (2002), 515-527  [abstract]

25.	S. Azam A presentation for reduced extended affine Weyl groups Comm. Algebra 28 (2000), 465-488  [abstract]

26.	S. Azam On the relation of extended affine Weyl groups and indefinite Weyl groups J. Algebra 222 (1999), 174-189  [abstract]