آمار
| تعداد نشریات | 6 |
| تعداد شمارهها | 123 |
| تعداد مقالات | 1,577 |
| تعداد مشاهده مقاله | 1,706,984 |
| تعداد دریافت فایل اصل مقاله | 1,590,203 |
Leavitt path algebras for order prime Cayley graphs of finite groups | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 3، دوره 10، شماره 4، اسفند 2025، صفحه 743-761 اصل مقاله (468.25 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28966.1798 | ||
| نویسندگان | ||
| Sumanta Das* ؛ Mridul Kanti Sen؛ Sunil kumar Maity | ||
| Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata-700019, India | ||
| چکیده | ||
| In this paper, we generalize the concept of Cayley graphs associated to finite groups. The aim of this paper is the characterization of graph theoretic properties of new type of directed graph $\Gamma_P(G;S)$ and algebraic properties of Leavitt path algebra of order prime Cayley graph $O\Gamma(G;S)$, where $G$ is a finite group with a generating set $S$. We show that the Leavitt path algebra of order prime Cayley graph $L_K(O\Gamma(G;S))$ of a non trivial finite group $G$ with any generating set $S$ over a field $K$ is a purely infinite simple ring. Finally, we prove that the Grothendieck group of the Leavitt path algebra $L_K(\Gamma_P(D_n;S))$ is isomorphic to $\mathbb{Z}_{2n-1}$, where $D_n$ is the dihedral group of degree $n$ and $S=\left\{a, b\right\}$ is the generating set of $D_n$. | ||
| کلیدواژهها | ||
| Group؛ directed Cayley graph؛ order prime Cayley graph؛ Grothendieck group | ||
| مراجع | ||
|
[1] G. Abrams, P. Ara, and M.S. Molina, Leavitt Path Algebras. Lecture Notes in Mathematics, vol. 2191, Springer-Verlag, London, 2017.
[2] G. Abrams and G.A. Pino, The Leavitt path algebra of a graph, J. Algebra 293 (2005), no. 2, 319–334. https://doi.org/10.1016/j.jalgebra.2005.07.028
[3] G. Abrams and B. Schoonmaker, Leavitt Path Algebras of Cayley Graphs Arising from Cyclic Groups, In Noncommutative Rings and their Applications (S. Dougherty, A. Facchini, A. Leroy, E. Puczylowski, and P. Solé, eds.), Con- temporary Mathematics, United States of America, 2015, pp. 1–10. [4] P. Ara, M.A. Moreno, and E. Pardo, Nonstable K-theory for graph algebras, Algebras Represent. Theory 10 (2007), no. 2, 157–178. https://doi.org/10.1007/s10468-006-9044-z
[5] P. Ara and E. Pardo, Stable rank of Leavitt path algebras, Proc. Am. Math. Soc. 136 (2008), no. 7, 2375–2386.
[6] M.R. Darafsheh and N.S. Poursalavati, On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups, SUT J. Math. 37 (2001), no. 1, 1–17. https://doi.org/10.55937/sut/1017153423
[7] S. Das, M.K. Sen, and S.K. Maity, Leavitt path algebras for power graphs of finite groups, J. Algebra Appl. 21 (2022), no. 10, Article ID: 2250209. https://doi.org/10.1142/S0219498822502097
[8] S. Das, M.K. Sen, and S.K. Maity, Grothendieck groups of purely infinite simple Leavitt path algebras for punctured power graphs of finite groups, J. Algebra Appl. 22 (2023), no. 11, Article ID: 2350234. https://doi.org/10.1142/S0219498823502341
[9] J. Gallian, Contemporary Abstract Algebra, Seventh Edition, Chapman and Hall/CRC, 2010.
[10] G. James and M. Liebeck, Representations and Characters of Groups, Second Edition, Cambridge University Press, Cambridge, 2001.
[11] H. Larki and A. Riazi, Stable rank of Leavitt path algebras of arbitrary graphs, Bull. Aust. Math. Soc. 88 (2013), no. 2, 206–217. https://doi.org/10.1017/S0004972712000913
[12] W.G. Leavitt, The module type of a ring, Trans. Am. Math. Soc. 103 (1962), no. 1, 113–130.
[13] R. Mohan, Leavitt path algebras of weighted Cayley graphs Cn(s, w), Proc. Math. Sci. 131 (2021), no. 2, Article ID: 17 https://doi.org/10.1007/s12044-021-00610-1
[14] T.G. Nam and N.T. Phuc, The structure of Leavitt path algebras and the invariant basis number property, J. Pure Appl. Algebra 223 (2019), no. 11, 4827–4856. https://doi.org/10.1016/j.jpaa.2019.02.017
[15] T.G. Nam and N.T. Phuc, On Leavitt path algebras of Hopf graphs, Acta Math. Vietnam. 48 (2023), no. 4, 533–549. https://doi.org/10.1007/s40306-023-00511-7 | ||
|
آمار تعداد مشاهده مقاله: 766 تعداد دریافت فایل اصل مقاله: 1,521 |
||