Klaus M Lux

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Journals/Publications

• Lux, K. M., Breuer, T., Hiss, G., & Luebeck, F. (2019). The completion of the 3-modular character table of the chevalley group F4(2) and its covering group. Mathematics of Computation.
• Lux, K. M. (2017). The 13-modular character table of 2.Suz.2. Communications in Algebra.
• Lux, K. M. (2017). The 3-modular 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), 3056-3070.
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  Abstract: 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 Frobenius-Schur 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, 140-157.
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  Abstract: 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 5-modular characters of the sporadic simple Harada-Norton group HN and its automorphism group HN.2. Journal of Algebra, 319(1), 320-335.
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  Abstract: We determine the 5-modular character table of the sporadic simple Harada-Norton group HN and its automorphism group HN . 2 using The Meat-Axe and condensation. © 2007 Elsevier Inc. All rights reserved.
• Lux, K. M., & Sźoke, M. (2007). Computing decompositions of modules over finite-dimensional algebras. Experimental Mathematics, 16(1), 1-6.
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  Abstract: Based on our method for determining endomorphism rings [Lux and Szoke 03], we describe an algorithm to compute decompositions of modules of finite-dimensional algebras over finite fields. The algorithm is implemented in the C-Meat-Axe [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), 91-98.
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  Abstract: We describe an algorithm to compute homomorphism spaces between modules of finite dimensional algebras over finite fields. The algorithm is implemented in the C-Meat-Axe.
• Lux, K., & Wiegelmann, M. (2001). Determination of Socle Series using the Condensation Method. Journal of Symbolic Computation, 31(1-2), 163-178.
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  Abstract: We show how the condensation method introduced by R. A. Parker can be applied to determine the socle series of a finite-dimensional 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), 373-381.
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  Abstract: We show that the Holt-Rees 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 Holt-Rees 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), 83-95.
• Cooperman, G., Hiss, G., Lux, K., & Müller, J. (1997). The Brauer tree of the principal 19-block of the sporadic simple Thompson group. Experimental Mathematics, 6(4), 293-300.
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  Abstract: 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 multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups. Communications in Algebra, 24(7), 2293-2316.
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  Abstract: In this paper, we classify all the multiplicity-free 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 2-modular Decomposition Matrices of the Non-principal Blocks of Maximal Defect of the Triple Cover of the Sporadic Simple McLaughlin Group. Journal of Symbolic Computation, 19(6), 585-600.
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  Abstract: The calculation of the modular character tables of 3.McL is completed by the determination of the 2-modular decomposition numbers of the faithful irreducible ordinary characters of 3.McL. The results are obtained by using the computer algebra systems MOC, Meat-Axe 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 Meat-Axe. Journal of Symbolic Computation, 17(6), 529-544.
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  Abstract: 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 MEAT-AXE 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), 285-306.
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  Abstract: 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 r-modular 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, Meat-Axe) has been made. © 1991 Springer-Verlag.
• Hiss, G., Lux, K., & Parker, R. (1991). The 5-modular characters of the McLaughlin group and its covering group. Manuscripta Mathematica, 73(1), 91-114.

Proceedings Publications

• Lux, K. M. (2019, 11/Fall). The 3-modular 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.