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IJMSI 2024, 19(2): 189-194 |
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Abdollahi A, Soleimani Malekan M. A Necessary Condition for Zero Divisors in Complex Group Algebra of Torsion-Free Groups. IJMSI 2024; 19 (2) :189-194
URL: http://ijmsi.ir/article-1-2047-en.html
URL: http://ijmsi.ir/article-1-2047-en.html
Abstract:
It is proved that if $sum_{gin G} a_g g$ is a non-zero zero divisor element of the complex group algebra $mathbb{C}G$ of a torsion-free group G then $2sum_{gin G} |a_g|^2<big( sum_{gin G} |a_g|big)^2$.
Keywords: Hilbert space $ell^2(G)$, Complex group algebras, Zero divisor conjecture, Torsion-free groups.
Type of Study: Research paper |
Subject:
General
References
1. K. A. Brown, On Zero Divisors in Group Rings, Bull. Lond. Math. Soc., 8, (1976), 251-256. [DOI:10.1112/blms/8.3.251]
2. J. M. Cohen, Zero Divisors in Group Rings, Comm. Algebra, 2, (1974), 1-14. [DOI:10.1080/00927877408822001]
3. T. Delzant, Sur lanneau Dun Groupe Hyperbolique, C. R. Acad. Sci. Paris Ser. I Math, 324(4), (1997), 381-384. [DOI:10.1016/S0764-4442(97)80071-7]
4. G. Elek, On the Analytic Zero Divisor Conjecture of Linnell, Bulletin of the London Mathematical Society, 35(2), (2003), 236-238. [DOI:10.1112/S002460930200173X]
5. D. R. Farkas, R. L. Snider, K0 and Noetherian Group Rings, J. Algebra, 42, (1976), 192-198. [DOI:10.1016/0021-8693(76)90036-3]
6. E. Formanek, The Zero Divisor Question for Supersolvable Groups, Bull. Aust. Math. Soc., 73c, (1973), 67-71. [DOI:10.1017/S000497270004288X]
7. P. A. Linnell, Zero Divisors and Group von Neumann Algebras, Pacific J. Math., 149, (1991), 349-363. [DOI:10.2140/pjm.1991.149.349]
8. P. A. Linnell, Division Rings and Group von Neumann Algebras, Forum Math., 5(6), (1993), 561-576. [DOI:10.1515/form.1993.5.561]
9. P. A. Linnell, Analytic Versions of the Zero Divisor Conjecture, In Geometry and cohomology in group theory (Durham 1994), 252. London Math. Soc. Lecture Note, 1998. [DOI:10.1017/CBO9780511666131.015]
10. P. A. Linnell, P. H. Kropholler, J. A. Moody, Applications of a New K-theoretic Theorem to Soluble Group Rings, Proc. Amer. Math. Soc., 104, (1988), 675-684. [DOI:10.1090/S0002-9939-1988-0964842-0]
11. A. I. Malcev, On Embedding of Group Algebras in a Division Algebra (in russian), Dokl. Akad. Nauk., 60, 1948, 1499-1501.
12. B. H. Neumann, On Ordered Division Rings, Trans. Amer. Math. Soc., 66, (1949), 202-252. [DOI:10.1090/S0002-9947-1949-0032593-5]
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