Uzi Vishne

                                 Publications


0. Central Simple Algebras, PhD thesis, Bar-Ilan University. Submitted: 7/2000, Approved: 4/2001.
My thesis deals with several topics in central simple algebras.
The first chpater is mainly on p-algebras of exponent p.
The second chpater is a detailed study of the Brauer algebra, focusing on the case of exponent=p.
The third chapter is essencially item [6] below.
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1. Factorization of Trinomials over Galois Fields of Characteristic $2$, Finite Fields and Their Applications, Vol. 3(4), 370-377, (1997).
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2. Mixing and Covering in the Symmetric Groups, Journal of Algebra, Vol. 205(1), 119-140, (1998).
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3. Primitive Algebras of Arbitrary Gelfand-Kirillov Dimension, Journal of Algebra, Vol. 211(1), 150-158, (1999).
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4. Polynomial Identities of $2\times 2$ matrices over the Grassmannian, Communications in Algebra, Vol. 30(1), 443-454, (2002).
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5. Efficient linear feedback shift registers with maximal period, with B. Tsaban, Finite Fields and Applications, Vol. 8(2), 256-267, (2002).
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6. Generators of central simple $p$-Algebras of Degree $3$, Israel J. Math., Vol. 129, 175-188, (2002).
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7. Classes of Wiring Diagrams and their invariants, with D. Garber and M. Teicher, Journal of Knot Theorey and its Ramifications, Vol. 11(8), 1165-1191, (2002).
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8. The Fundamental Group of a Galois cover of ${\mathbb CP}^1\times {\mathbb T}$, with M. Amram, D. Goldberg and M. Teicher, Algebraic and Geometric Topology, Vol. 2, 403-432, (2002).
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9. $\pi_1$-classification of real arrangements with up to eight lines, with M. Teicher and D. Garber, Topology, Vol. 42(1), 265-289, (2003).
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10. Dihedral crossed products of exponent $2$ are Abelian, Archiv. der Math., Vol. 80(2), 119-122, (2003).
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11. Galois cohomology of fields without roots of Unity, Journal of Algebra, Vol. 279(2), 451-492, (2004).
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12. Coxeter Covers of the Symmetric Groups, with L.H. Rowen and M. Teicher, J. Group Theory, Vol. 8, 139-169, (2005).
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13. Explicit construction of Ramanujan complexes of type $\tilde{A_d}$, with A. Lubotzky and B. Samuels, European J. of Combinatorics, Vol. 26(6), 965-993, (2005).
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14. Ramanujan complexses of type $\tilde{A_d}$, with A. Lubotzky and B. Samuels, Israel J. Math., Vol. 149, 267-300, (2005).
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15. Triviality of the functor $\operatorname{Coker}(K_1(F)\rightarrow K_1(D))$ for division algebras, with R. Hazrat, Communications in Algebra, Vol. 33, 1427-1435, (2005).
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16. Probabilistic Solutions of equations in the braid group , with D. Garber, S. Kaplan, M. Teicher and B. Tsaban, Advances in Applied Mathematics, Vol. 35(3), 323-334, (2005).
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17. An affine prime non-semiprimitive monomial algebra with quadratic growth, with A. Smoktunowicz, Advances in Applied Mathematics, Vol. 37, 511-513, (2006).
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18. The Coxeter quotient of the fundamental group of the Galois cover of ${\mathbb T} \times {\mathbb T}$, with M. Amram and M. Teicher, Communications in Algebra, Vol. 34, 89-106, (2006).
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19. Division algebras and noncommensurable isospectral Manifolds, with A. Lubotzky and B. Samuels, Duke J. Math., Vol. 135(2), 361-379, (2006).
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20. Isospectral Cayley graphs of some finite simple groups, with A. Lubotzky and B. Samuels, Duke J. Math., Vol. 135, 381-393, (2006).
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21. Length-based conjugacy search in the braid Group, with D. Garber, S. Kaplan, M. Teicher and B. Tsaban, Contemporary Mathematics, Vol. 418, 75-87, (2006).
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22. Pattern Matching with Address Error: Rearrangement Distances, with Amihood Amir et. al., Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 1221-1229, (2006).
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23. Normal bases of PI-algebras, with A. Belov and L.H. Rowen, Advances in Applied Mathematics, Vol. 37(3), 378-389, (2006).
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24. Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups, with M. Katz and M. Schaps, J. of Differenital Geom., Vol. 76(3), 399-422, (2007).
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25. The fundamental group of the Galois cover for Hirzebruch surface $F_1(2,2)$, with M. Amram, M. Teicher, International J. Algebra and Computation, Vol. 17(3), 507-525, (2007).
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26. The fundamental group of Galois cover of ${\mathbb T} \times {\mathbb T}$, with M. Amram and M. Teicher, International J. Algebra and Computation, Vol. 18(8), 1259-1282, (2008).
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27. Pattern Matching with Address Error: Rearrangement Distances, with Amihood Amir et. al., Journal of Computers and Systems Sciences, Vol. 75(6), 359-370, (2009).

28. Kneser-Tits Problem for trialitarian groups and bounded generation by restricted elements, with Ph. Gille, Oberwolfach Proceedings series, 1407-1410, (2009).
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29. Structure of Zariski closed algebras, with A. Belov and L. Rowen, Transactions of the AMS, Vol. 362(9), 4695-4734, (2010).
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30. An Azumaya algebra version of the Kneser-Tits problem for groups of type~${}^{3,6}D_4$, with L.H. Rowen, D. Saltman and Y. Segev, Comm. Alg., Vol. 39(1), 133-152, (2011).

31. Open problems on Central Simple Algebras, with Asher Auel, Eric Brussel and Skip Garibaldi, Transformation Groups, Vol. 16(1), 219-264, (2011).
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32. Characters and the number of solutions to equations in Groups, with A. Amit, Journal of Algebra and Its Applications, Vol. 10(4), 675-686, (2011).
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33. Application of full quivers of representations of algebras, to polynomial identities, with A. Belov and L. Rowen, Communications in Algebra, Vol. 39, 4536-4551, (2011).
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34. Polynomial Identities of $M_{2,1}(G)$, Comm. Alg., Vol. 39(6), 2044-2050, (2011).
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35. Hurwitz quaternion order and arithmetic Riemann surfaces, with M. Katz and M. Schaps, Geometriae Dedicata, Vol. 155(1), 151-161, (2011).
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36. Isotropic subspaces in symmetric composition algebras and Kummer subspaces in central simple algebras of degree $3$, with E. Matrzi, Manuscripta Mathematica, Vol. 137(3), 497-523, (2012).
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37. Non-cyclic algebras with $n$-central elements, with Eli Matzri and Louis Rowen, Vol. 140(2), 513-518, accepted to Proceedings of the AMS (2012).
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38. Artin covers of the braid groups, with M. Amram and R. Lawrence, Journal of Knots and their Ramifications, Vol. 21(7), 46 pp., (2012).
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39. Full quivers of representations of algebras, with A. Belov and L. Rowen, Transactions of the AMS, Vol. 364, 5525-5569, (2012).
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40. Full exposition of Specht's problem, with A. Belov and L.H. Rowen, Serdica Math J., Vol. 38, 313-370, (2012).

41. Clifford algebras of binary homogeneous forms, with Adam Chapman, Journal of Algebra, Vol. 366, 94-111, (2012).
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42. Confidence Interval for Risk Score Index, with Kenneth Hochberg, Amir Sandach and Mitchell Snyder, Methodology and Computing in Applied Probability, Vol. 15(4), 987-1002, (2013).

43. Admissibility under extension of number fields, with D. Neftin, Documenta Mathematica, Vol. 18, 359-382, (2013).
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44. Stiefel-Whitney Invariants for Bilinear Forms, with Uriya First, Linear Algebra and its Applications, Vol. 439, 1905-1917, (2013).
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45. PI-varieties associated to full quivers of representations of algebras, with A. Belov and L.H. Rowen, Transactions of the AMS, Vol. 365(5), 40 pp., (2013).

46. Square-central elements and standard generators for biquaternion algebras, with A. Chapman, Israel J. Math., Vol. 197, 409-423, (2013).

47. Composition algebras and cyclic $p$-algebras in characteristic $3$, with Eli Matzri, Manuscripta Mathematica, Vol. 143(1), 1-18, (2014).
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48. Zariski closed algebras in varieties of universal algebra, with L.H. Rowen and A. Giambruno, Journal of Algebra and Rep. Theory, Vol. 17, 11 pp., (2014).
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49. Specht's problem for associative affine algebras over commutative Noetherian rings, with A. Belov and L.H. Rowen, Transactions of the AMS, Vol. 367(8), 5553-5596, (2015).
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50. Bolza quaternion order and asymptotics of systoles along congruence subgroups, with Karin Katz, Mikhail Katz and Michael Schein, Experimental Mathematics, Vol. 25(4), (2016).
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51. Bimodule strucutre of central simple algebras, with Eliyahu Matzri, Louis Rowen, David Saltman, Journal of Algebra, Vol. 471, 454-479, (2016).
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52. Kummer Spaces in Cyclic Algebras of Prime Degree, with Adam Chapman, David J. Grynkiewicz, Eliyahu Matzri and Louis H. Rowen, J Pure Appl Alg, Vol. 220, (2016).
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53. Linkage of Quadratic Pfister Forms, with Adam Chapman and Shira Gilat, Communications in Algebra, Vol. 12, 5212-5226, (2017).
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54. Union of chains of primes, with Beeri Greenfeld and L.H. Rowen, accepted to J Pure Appl Alg.

55. Generalized sign and the Grassmann algebra in arbitrary characteristic, with Gal Dor, Alexei Belov, 26 pp., submitted.
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56. Decomposing the Quaternion Fourier transform, with Adam Chapman, submitted.

57. Decomposability and relative symbol length of central simple algebras, with Elyiahu Matzri and Louis Rowen, submitted.

58. Field of definition for admissible groups, with D. Neftin, 11 pp., submitted.
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Last updated: 30 Aug 2017