چند جمله‌ای‌های هال برای جبرهای $2$-ناکایاما

نوع مقاله : مقاله پژوهشی

نویسنده

گروه ریاضی محض، دانشکده ریاضی و آمار، دانشگاه اصفهان، اصفهان، ایران

چکیده

در این مقاله نشان می‌دهیم برای جبرهای متناهی بعد $2$-ناکایامای راست, چند جمله‌ای‌های هال وجود دارند. این مطلب حدس رینگل را برای جبرهای $2$-ناکایامای راست اثبات می‌کند.

کلیدواژه‌ها


[1] I. Assem, D. Simson and A. Skowronski, Elements of the Representation Theory of Associative Algebra, Techniques of repre-sentation theory, 1, London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006.
[2] J. A. Green, Hall algebras, hereditary algebras and quantum groups, Invent. Math., 120 (1995) 361–377.
[3] A. Hubery, Hall polynomials for affine quivers, Represent. Theory, 14 (2010) 355–378.
[4] I. G. Macdonald, Symmetric functions and Hall polynomials, Second edition. With contributions by A. Zelevinskyi Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995.
[5] A. Nasr-Isfahani, Hall polynomials and composition algebra of representation finite algebras, Algebr. Represent. Theory, 17 (2014) 1155–1161.
[6] A. Nasr-Isfahani, Hall polynomials for Nakayama algebras, Algebr. Represent. Theory, 15 (2012) 483–490.
[7] A. Nasr-Isfahani and M. Shekari, Right n-Nakayama algebras and their representations, Algebr. Represent. Theory, 23 (2020) 1297–1317.
[8] C. M. Ringel, From representation of quivers via Hall and Loewy algebras to quantum groups, Contemp. Math., 131 (1992) 381–401.
[9] C. M. Ringel, Green’s theorem on Hall algebras, Representation theory of algebras and related topics (Mexico City, 1994), 19 (1996) 185–245.
[10] C. M. Ringel, Hall algebras, in Topics in Algebra, part I, Banach Centre Publ., PWN, Warsaw, 26 (1990) 433–447.
[11] C. M. Ringel, Hall algebras and quantum groups, Invent. Math., 101 (1990) 583–591.
[12] C. M. Ringel, Hall polynomials for the representation-finite hereditary algebras, Adv. Math., 84 (1990) 137–178.
[13] C. M. Ringel, Lie algebras arising in representation theory, in, London Math. Soc. Lecture Note Ser., Cambridge Univ. Press, Cambridge, UK, 168 (1992) 284–291.
[14] C. M. Ringel, The Theorem of Bo Chen and Hall polynomials, Nagoya Math. J., 183 (2006) 143–160.
[15] B. Sevenhant and M. Van den Bergh, A relation between a conjecture of Kac and the structure of the Hall algebra, J. Pure Appl. Algebra, 160 (2001) 319–332.
[16] S. Zhang, The Hall polynomials for tame quiver algebras, J. Algebra, 239 (2001) 606–614.