Klaus M Lux
 Professor, Mathematics
 Member of the Graduate Faculty
Contact
 (520) 6216856
 Environment and Natural Res. 2, Rm. S335
 Tucson, AZ 85719
 klux@arizona.edu
Bio
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Interests
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Courses
202324 Courses

Dissertation
MATH 920 (Spring 2024) 
Independent Study
MATH 499 (Spring 2024) 
Independent Study
MATH 599 (Spring 2024) 
Intro To Cryptography
MATH 445 (Spring 2024) 
Dissertation
MATH 920 (Fall 2023) 
Independent Study
MATH 599 (Fall 2023) 
Intro to Linear Algebra
MATH 313 (Fall 2023) 
Topics In Algebra
MATH 518 (Fall 2023)
202223 Courses

Dissertation
MATH 920 (Spring 2023) 
Group Theory
MATH 517B (Spring 2023) 
Honors Thesis
MATH 498H (Spring 2023) 
Dissertation
MATH 920 (Fall 2022) 
Group Theory
MATH 517A (Fall 2022) 
Honors Thesis
MATH 498H (Fall 2022) 
Intro to Linear Algebra
MATH 313 (Fall 2022)
202122 Courses

Algebra
MATH 511B (Spring 2022) 
Directed Research
MATH 492 (Spring 2022) 
Dissertation
MATH 920 (Spring 2022) 
Independent Study
MATH 599 (Spring 2022) 
Algebra
MATH 511A (Fall 2021) 
Dissertation
MATH 920 (Fall 2021) 
Independent Study
MATH 599 (Fall 2021) 
Intro to Linear Algebra
MATH 313 (Fall 2021)
202021 Courses

Dissertation
MATH 920 (Spring 2021) 
Group Theory
MATH 517B (Spring 2021) 
Honors Thesis
MATH 498H (Spring 2021) 
Research Tutorial Group
MATH 596G (Spring 2021) 
Dissertation
MATH 920 (Fall 2020) 
Group Theory
MATH 517A (Fall 2020) 
Honors Thesis
MATH 498H (Fall 2020) 
Independent Study
MATH 599 (Fall 2020) 
Intro to Linear Algebra
MATH 313 (Fall 2020)
201920 Courses

Dissertation
MATH 920 (Spring 2020) 
Directed Research
MATH 492 (Fall 2019) 
Independent Study
MATH 599 (Fall 2019) 
Topics In Algebra
MATH 518 (Fall 2019)
201819 Courses

Algebra
MATH 511B (Spring 2019) 
Dissertation
MATH 920 (Spring 2019) 
Group Theory
MATH 517B (Spring 2019) 
Independent Study
MATH 599 (Spring 2019) 
Algebra
MATH 511A (Fall 2018) 
Dissertation
MATH 920 (Fall 2018) 
Group Theory
MATH 517A (Fall 2018) 
Independent Study
MATH 599 (Fall 2018)
201718 Courses

2nd Crs Abstract Algebra
MATH 415B (Spring 2018) 
2nd Crs Abstract Algebra
MATH 515B (Spring 2018) 
Dissertation
MATH 920 (Spring 2018) 
Independent Study
MATH 599 (Spring 2018) 
Intro to Linear Algebra
MATH 313 (Spring 2018) 
Calculus I SI Seminar
MATH 196M (Fall 2017) 
Discrete Math Cmptr Sci
MATH 243 (Fall 2017) 
Dissertation
MATH 920 (Fall 2017) 
Independent Study
MATH 599 (Fall 2017) 
Intro Abstract Algebra
MATH 415A (Fall 2017) 
Intro Abstract Algebra
MATH 515A (Fall 2017) 
Intro to Linear Algebra
MATH 313 (Fall 2017)
201617 Courses

Dissertation
MATH 920 (Spring 2017) 
Honors Thesis
MATH 498H (Spring 2017) 
Group Theory
MATH 517A (Fall 2016) 
Honors Thesis
MATH 498H (Fall 2016) 
Independent Study
MATH 599 (Fall 2016) 
Intro Abstract Algebra
MATH 415A (Fall 2016) 
Intro Abstract Algebra
MATH 515A (Fall 2016)
201516 Courses

Algebra
MATH 511B (Spring 2016) 
Honors Thesis
MATH 498H (Spring 2016) 
Independent Study
MATH 599 (Spring 2016)
Scholarly Contributions
Journals/Publications
 Lux, K. M., Breuer, T., Hiss, G., & Luebeck, F. (2019). The completion of the 3modular character table of the chevalley group F4(2) and its covering group. Mathematics of Computation.
 Lux, K. M. (2017). The 13modular character table of 2.Suz.2. Communications in Algebra.
 Lux, K. M. (2017). The 3modular characters of the FIscher group Fi23. Journal of Experimental Mathematics.
 Lux, K. M. (2016). Cohomology of SL_2 and related structures.. Communications in Algebra.
 Lux, K., Fry, A. S., & Vinroot, C. R. (2012). Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups. Communications in Algebra, 40(8), 30563070.More infoAbstract: Let W be a finite Coxeter group, P a parabolic subgroup of W, and N W(P) the normalizer of P in W. We prove that every element in N W(P) is strongly real in N W(P), and that every irreducible complex character of N W(P) has FrobeniusSchur indicator 1. © 2012 Copyright Taylor and Francis Group, LLC.
 Lux, K., Neunhöffer, M., & Noeske, F. (2012). Condensation of homomorphism spaces. LMS Journal of Computation and Mathematics, 15, 140157.More infoAbstract: We present an efficient algorithm for the condensation of homomorphism spaces. This provides an improvement over the known tensor condensation method which is essentially due to a better choice of bases. We explain the theory behind this approach and describe the implementation in detail. Finally, we give timings to compare with previous methods. Copyright © London Mathematical Society 2012.
 Lux, K., Noeske, F., & Ryba, A. J. (2008). The 5modular characters of the sporadic simple HaradaNorton group HN and its automorphism group HN.2. Journal of Algebra, 319(1), 320335.More infoAbstract: We determine the 5modular character table of the sporadic simple HaradaNorton group HN and its automorphism group HN . 2 using The MeatAxe and condensation. © 2007 Elsevier Inc. All rights reserved.
 Lux, K. M., & Sźoke, M. (2007). Computing decompositions of modules over finitedimensional algebras. Experimental Mathematics, 16(1), 16.More infoAbstract: Based on our method for determining endomorphism rings [Lux and Szoke 03], we describe an algorithm to compute decompositions of modules of finitedimensional algebras over finite fields. The algorithm is implemented in the CMeatAxe [Ringe 94]. © A K Peters, Ltd.
 Lux, K. M., & Szoke, M. (2003). Computing Homomorphism Spaces between Modules over Finite Dimensional Algebras. Experimental Mathematics, 12(1), 9198.More infoAbstract: We describe an algorithm to compute homomorphism spaces between modules of finite dimensional algebras over finite fields. The algorithm is implemented in the CMeatAxe.
 Lux, K., & Wiegelmann, M. (2001). Determination of Socle Series using the Condensation Method. Journal of Symbolic Computation, 31(12), 163178.More infoAbstract: We show how the condensation method introduced by R. A. Parker can be applied to determine the socle series of a finitedimensional representation of a group over a finite field. We develop several new techniques for this approach and illustrate their power by the example of the socle series of all projective indecomposable representations of the sporadic simple Mathieu group M23in characteristic 2. © 2001 Academic Press.
 Ivanyos, G., & Klaus, L. (2000). Treating the exceptional cases of the MeatAxe. Experimental Mathematics, 9(3), 373381.More infoAbstract: We show that the HoltRees extension of the standard MeatAxe procedure finds submodules of modules over finite algebras with positive probability in more cases than originally claimed. For the case when the HoltRees method fails we propose a further, but still simple and efficient extension.
 Héthelyi, L., Szöke, M., & Lux, K. (1998). The restriction of indecomposable modules of group algebras and the quasi green correspondence. Communications in Algebra, 26(1), 8395.
 Cooperman, G., Hiss, G., Lux, K., & Müller, J. (1997). The Brauer tree of the principal 19block of the sporadic simple Thompson group. Experimental Mathematics, 6(4), 293300.More infoAbstract: This paper completes the construction of the Brauer tree of the sporadic simple Thompson group in characteristic 19. Our main computational tool to arrive at this result is a new parallel implementation of the DirectCondense method.
 Breuer, T., & Lux, K. (1996). The multiplicityfree permutation characters of the sporadic simple groups and their automorphism groups. Communications in Algebra, 24(7), 22932316.More infoAbstract: In this paper, we classify all the multiplicityfree permutation characters of sporadic simple groups and their automorphism groups. This project is an application of the group theory system GAP, its character table library, and its library of tables of marks. Copyright © 1996 by Marcel Dekker, Inc.
 Hiss, G., Lux, K., & Müller, J. (1995). The 2modular Decomposition Matrices of the Nonprincipal Blocks of Maximal Defect of the Triple Cover of the Sporadic Simple McLaughlin Group. Journal of Symbolic Computation, 19(6), 585600.More infoAbstract: The calculation of the modular character tables of 3.McL is completed by the determination of the 2modular decomposition numbers of the faithful irreducible ordinary characters of 3.McL. The results are obtained by using the computer algebra systems MOC, MeatAxe and GAP, and by applying condensation methods. © 1995 Academic Press. All rights reserved.
 Lux, K., Müller, J., & Ringe, M. (1994). Peakword Condensation and Submodule Lattices: An Application of the MeatAxe. Journal of Symbolic Computation, 17(6), 529544.More infoAbstract: We describe a new condensation method for computing the submodule lattice of a module for a finite dimensional algebra over a finite field, which exploits the idea of condensation and extends it to the case of primitive idempotents. The method has been implemented in the new C version of the MEATAXE developed at Aachen, and we give several examples which have been analysed with our method. © 1994 Academic Press. All rights reserved.
 Geck, M., & Lux, K. (1991). The decomposition numbers of the hecke algebra of type F_{ 4}. Manuscripta Mathematica, 70(1), 285306.More infoAbstract: Let W be the finite Coxeter group of type F 4, and H r (q) be the associated Hecke algebra, with parameter a prime power q, defined over a valuation ring R in a large enough extension field of Q, with residue class field of characteristic r. In this paper, the rmodular decomposition numbers of H R (q) are determined for all q and r such that r does not divide q. The methods of the proofs involve the study of the generic Hecke algebra of type F 4 over the ring A = ℤ[u 1/2, u 1/2] of Laurent polynomials in an indeterminate u 1/2 and its specializations onto the ring of integers in various cyclotomic number fields. Substancial use of computers and computer program systems (GAP, MAPLE, MeatAxe) has been made. © 1991 SpringerVerlag.
 Hiss, G., Lux, K., & Parker, R. (1991). The 5modular characters of the McLaughlin group and its covering group. Manuscripta Mathematica, 73(1), 91114.
Proceedings Publications
 Lux, K. M. (2019, 11/Fall). The 3modular character table of the Automorphism group of the O'Nan group. In Springer Proc. Math. Stat., 277.
 Lux, K. M. (2017, 7/Fall). Finite Simple Groups: Thirty Years of the Atlas an Beyond. In International Conference: Finite Simple Groups: Thirty Years of the Atlas an Beyond, Princeton University.