Chia-Hsin Liu

Employment

• Professor, Department of Mathematics, National Taiwan Normal University, 2014-present.
• Associate Professor, Department of Mathematics, National Taiwan Normal University, 2002-2014.
• Assistant Professor, Department of Mathematics, National Taiwan Normal University, 2001-2002.
• Assistant Professor, Department of Applied Mathematics, National Sun Yet-sen University, 1999-2001.

Education

• Ph.D. University of Wisconsin-Madison, U.S.A., 1999
Thesis Advisor: Professor Donald S. Passman
Dissertation: Group identities, polynomial identities and generalized polynomial identities.
• M.A. University of Wisconsin-Madison, U.S.A., 1995
• B.S. National Taiwan University, Taipei, Taiwan, R.O.C., 1991

Research Interests

Publications ( abstracts )

1. Group algebras with units satisfying a group identity,
   Proc. Amer. Math. Soc. 127(1999), no. 2, 327--336.
2. Group algebras with units satisfying a group identity II, (with Donald S. Passman),
   Proc. Amer. Math. Soc. 127 (1999), no. 2, 337--341.
3. Group identities on units of locally finite algebras and twisted group algebras,
   Communications in Algebra 28 (2000), no. 10, 4783--4802.
4. Some properties on rings with units satisfying a group identity,
   Journal of Algebra 232 (2000), no. 1, 226--235.
   Errata
5. On nil subsemigroups of rings with group identities, (with K.I. Beidar and Wen-Fong Ke),
   Communications in Algebra 30 (2002), 347--352.
6. On units of twisted group algebras,
   Journal of Algebra 250 (2002), no. 1, 271--282.
7. Group identities and prime rings generated by units, (with Tsiu-Kwen Lee),
   Communications in Algebra 31 (2003), 3305--3309.
8. Automorphism groups of certain simple 2-(q,3,\lambda) designs constructed from finite fields , (with K.I. Beidar, W.-F. Ke and W.-R. Wu),
   Finite fields and Their Applications 9 (2003), 400--412.
9. Prime Lie rings of derivations of commutative rings in characteristic 2, (with Donald S. Passman),
   Journal of Algebra 311 (2007), no. 1, 352--364.
10. Semiprime Lie rings of derivations of commutative rings,
    Contemp. Math., 420, Amer. Math. Soc., 2006, 259--268.
11. Artinian Hopf algebras are finite dimensional, (with James J. Zhang),
    Proc. Amer. Math. Soc. 135 (2007), no. 6, 1679--1680.
12. Multiplicative Jordan decomposition in group rings of 3-groups, (with Donald S. Passman),
    Journal of Algebra and its applications 8 (2009), no. 4, 509--519.
13. Multiplicative Jordan decomposition in group rings of 2,3-groups, (with Donald S. Passman),
    Journal of Algebra and its applications 9 (2010), no. 3, 483--492.
14. Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal,
    Journal of Algebra 371 (2012), 300--313.
15. Multiplicative Jordan decomposition in group rings of 3-groups, II, (with Donald S. Passman),
    Communications in Algebra 42 (2014), 2633--2639.
16. Multiplicative Jordan decomposition in group rings with a Wedderburn component of degree 3, (with Donald S. Passman),
    Journal of Algebra 388 (2013), 203--218.
17. Groups with certain normality conditions, (with Donald S. Passman),
    Communications in Algebra 44 (2016), 3308--3323.

Teaching for Fall 2024

• Topics in representation theory Tue 9:10-12:10
• Algebra Mon 10:20-12:10, Thur 10:20-11:10
• Exploration of algebra Thur 11:20-12:10
• TopologyTue 13:20-15:10, Thur 9:10-10:00

Courses Taught

• Fall 1999, Topology, Calculus.
• Spring 2000, Ring theory, Calculus.
• Fall 2000, Topology, Calculus.
• Spring 2001, Algebra (Graduate), Algebra, Calculus.
• Fall 2001, Algebra (Graduate), Algebra, Calculus.
• Spring 2002, Algebra (Graduate), Algebra, Calculus.
• Fall 2002, Representation theory of finite groups, Special topics in algebra, Calculus.
• Spring 2003, Representation theory of finite groups, Advanced linear algebra, Calculus.
• Fall 2003, Algebra, Set theory, Special topics in algebra, Topics in representation theory, Independent study.
• Spring 2004, Algebra, Advanced linear algebra, Lie algebra, Independent study.
• Fall 2004, Topics in algebra, Set theory, Representation theory of finite groups.
• Spring 2005, Topics in algebra, Advanced linear algebra, Representation theory of finite groups.
• Fall 2005, Algebra, Lie algebra.
• Spring 2006, Algebra, Advanced linear algebra, Topics in representation theory.
• Fall 2006, Algebra (Graduate), Topics in algebra, Topics in group rings.
• Spring 2007, Algebra (Graduate), Topics in group rings, Number theory.
• Fall 2007, Algebra, Topics in algebra.
• Spring 2008, Algebra, Topics in algebra.
• Fall 2008, Ring theory, Topics in algebra.
• Spring 2009, Ring theory, Number theory.
• Fall 2009, Topics in group rings, Algebra.
• Spring 2010, Topics in group rings, Algebra.
• Fall 2010, Algebra (Graduate), Advanced linear algebra.
• Spring 2011, Algebra (Graduate), Advanced linear algebra.
• Fall 2011, Algebra, Introduction to mathematics.
• Spring 2012, Algebra, Number theory.
• Fall 2012, Introduction to mathematics, Calculus.
• Spring 2013, Number theory, Calculus.
• Fall 2013, Algebra, Exploration of algebra, Introduction to mathematics.
• Spring 2014, Algebra, Exploration of algebra, Number theory.
• Fall 2014, Algebra (Graduate), Topics in group rings.
• Spring 2015, Algebra (Graduate), Topics in group rings.
• Fall 2015, Character theory of finite groups, Algebra, Exploration of algebra.
• Spring 2016, Character theory of finite groups, Algebra, Exploration of algebra.
• Fall 2016, Lie algebra, Algebra, Exploration of algebra.
• Spring 2017, Topics on Lie algebra, Algebra, Exploration of algebra.
• Spring 2018, Advanced linear algebra, Units in group rings.
• Fall 2018, Algebra (Graduate), Algebraic topology.
• Spring 2019, Algebra (Graduate), Algebraic topology.
• Fall 2019, Algebra, Exploration of algebra, Introduction to mathematics.
• Spring 2020, Algebra, Exploration of algebra, Number theory.
• Fall 2020, Algebra (Graduate), Topics in algebra, Introduction to mathematics.
• Spring 2021, Character theory of finite groups, Special topics in algebra, Number theory.
• Fall 2021, Charcter theory of finite groups, Lie algebra, Algebra, Exploration of algebra.
• Spring 2022, Lie algebra, Algebra, Exploration of algebra, Number theory.
• Fall 2022, Algebra, Exploration of algebra, Algebra ( Graduate ).
• Spring 2023, Algebra, Exploration of algebra, Algebra ( Graduate ), Number theory.
• Fall 2023, Algebra, Exploration of algebra, Topics in group rings.
• Spring 2024, Algebra, Exploration of algebra, Topics in group rings, Number theory.
• Fall 2024, Algebra, Exploration of algebra, Topics in representation theory, Topology.

Talks

• Oct 3, 2015, Loyola University, Chicago, USA, International Conference on Groups, Rings, Group Rings and Hopf Algebras, (celebrating the 75th birthday of Donald S. Passman), SSN groups, NCN groups and multiplicative Jordan decomposition in group rings.
• Jun 12, 2015, National Taiwan University, One Day Workshop on Rings and Algebras, in Honor of Professor Chen-Lian Chuang, Multiplicative Jordan decomposition in group rings.
• May 22, 2015, National Chung Cheng University, Workshop on Algebra and Geometry, Groups with certain normality conditions.
• Jun 19, 2013, Academia Sinica, Multiplicative Jordan decomposition in group rings.
• Jun 7, 2013, National Taiwan University, Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal.
• Apr 27, 2013, National Chung Cheng University, Workshop on Algebra and Geometry, Multiplicative Jordan decomposition in group rings of 3-groups.
• Apr 28, 2012, National Chung Cheng University, Workshop on Algebra and Geometry, Multiplicative Jordan decomposition in group rings of 2-groups.
• May 27, 2011, National Taiwan University, Multiplicative Jordan decomposition in group rings of 2-groups.
• Apr 30, 2011, National Chung Cheng University, Workshop on Algebra and Geometry, Multiplicative Jordan decomposition in group rings of 2,3-groups.
• Oct 30, 2009, National Taiwan University, Multiplicative Jordan decomposition in group rings.
• Oct 19, 2009, National Tsing Hwa University, Multiplicative Jordan decomposition in group rings.
• Mar 13, 2009, National Taiwan University, Multiplicative Jordan decomposition in integral group rings.
• Oct 23, 2006, National Chengchi University, Lie algebras of derivations of commutative algebras.
• Apr 29, 2006, National Chung Cheng University, Workshop on Algebra and Geometry, Lie algebras of derivations of commutative algebras.
• Dec 16, 2005, National Taiwan University, Prime Lie rings of derivations of commutative rings.
• Apr 24, 2004, National Chung Cheng University, Workshop on Algebra and Geometry, Group identities and semiprime rings generated by units.
• Feb 12, 2004, Academia Sinica, Group identities, group algebras and rings generated by units.
• Apr 26, 2003, National Chung Cheng University, Workshop on Algebra and Geometry, Artinian Hopf algebras.
• Feb 24, 2003, National Taiwan University, Artinian Hopf algebras.
• Apr 28, 2002, National Chung Cheng University, Workshop on Algebra and Geometry, Group identities and rings generated by units.
• Mar 27, 2002, National Taiwan Normal University, Hartley's problem and rings generated by units.
• Nov 30, 2001, National Taiwan University, Group identities and prime rings generated by units.
• Aug 14, 2001, University of Washington, On rings whose units satisfy a group identity.
• Apr 15, 2001, National Chung Cheng University, Seminar on Algebra, Group identities on units of twisted group algebras.
• Feb 14, 2001, National Taiwan Normal University, Units of twisted group algebras.
• Jan 15, 2001, National Taiwan University, Seminar of Algebra and Geometry, Units of group algebras and twisted group algebras.
• Dec 9, 2000, Tamkang University, Annual Meeting of Mathematical Society of ROC, Nilpotent elements in GI-rings and Koethe conjecture.
• Nov 11, 2000, National Sun Yat-sen University, Some properties on rings with units satisfying a group identity.
• Jun 20, 2000, National Taiwan University, Group identities, nilpotent elements and Koethe conjecture.
• Mar 29, 2000, Chinese University of Hong Kong, Workshop in Algebra and Discrete Mathematics, Group identities on units of rings.
• Dec 17, 1999, National Chiao Tung University, Algebras with units satisfying a group identity.
• Dec 12, 1999, Fu Jen Catholic University, Annual Meeting of Mathematical Society of ROC, Rings with units satisfying a group identity.
• Dec 8, 1999, National Chung Cheng University, Algebras with units satisfying a group identity.
• Nov 25, 1999, National Taiwan University, Some properties on rings with units satisfying a group identity.
• Apr 16, 1999, National Sun Yat-sen University, Group algebras with units satisfying a group identity.
• Apr 14, 1999, National Taiwan Normal University, Group algebras with units satisfying a group identity.
• Apr 13, 1999, Fu Jen Catholic University, Group algebras with units satisfying a group identity.
• Jan 7, 1999, National Cheng Kung University.
• Jan 6, 1999, National Chung Cheng University.
• Jan 5, 1999, National Chiao Tung University.
• Jan 4, 1999, National Taiwan University.
• Dec 30, 1998, National Tsing Hwa University.
• Jul 1997, National Taiwan University.
• 1997-1998, several talks in the ring theory seminar, Department of Mathematics, University of Wisconsin-Madison, USA.

Awards and Honors