On the combinatorics of extensions of preinjective Kronecker modules

[1] I. Assem, D. Simson, A. Skowro´nski, Elements of the representation theory of associative algebras, Vol. 1, Techniques of representation theory, London Mathematical Society Student Texts 65, Cambridge University Press, Cambridge, 2006.10.1017/CBO9780511614309Search in Google Scholar

[2] M. Auslander, I. Reiten, S. Smalo, Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, No. 36, Cambridge University Press, 1995.10.1017/CBO9780511623608Search in Google Scholar

[3] M. Dodig, Completion up to a matrix pencil with column minimal indices as the only nontrivial Kronecker invariants, Linear Algebra Appl., 438 (2013), 3155-3173.10.1016/j.laa.2012.12.040Search in Google Scholar

[4] M. Dodig, M. Stošić, Combinatorics of column minimal indices and matrix pencil completion problems, SIAM J. Matrix Anal. Appl., 31 (2010), 2318-2346.10.1137/090747853Search in Google Scholar

[5] M. Dodig, M. Stošić, On convexity of polynomial paths and generalized majorizations, Electron. J. Combin., 17 (1) (2010), R61.10.37236/333Search in Google Scholar

[6] M. Dodig, M. Stošić, On properties of the generalized majorization, Electron. J. Linear Algebra, 26 (2013), 471-509.10.13001/1081-3810.1665Search in Google Scholar

[7] F. R. Gantmacher, Matrix theory, Vol. 1 and 2, Chelsea, New York, 1974.Search in Google Scholar

[8] Y. Han, Subrepresentations of Kronecker representations, Linear Algebra Appl., 402 (2005), 150-164.10.1016/j.laa.2004.12.015Search in Google Scholar

[9] J. J Loiseau, S. Mondi´e, I. Zaballa, P. Zagalak, Assigning the Kronecker invariants of a matrix pencil by row or column completions, Linear Algebra Appl., 278 (1998), 327-336.10.1016/S0024-3795(97)10089-1Search in Google Scholar

[10] I. Macdonald, Symmetric Functions and Hall Polynomials, Second edition, Clarendon Press, Oxford, 1995.Search in Google Scholar

[11] M. Reineke, The monoid of families of quiver representations, Proc. Lond. Math. Soc., 84 (2002), 663-685.10.1112/S0024611502013497Search in Google Scholar

[12] C. M. Ringel, Tame algebras and integral quadratic forms, Lecture Notes in Mathematics, No. 1099, Springer-Verlag, Berlin, 1984.Search in Google Scholar

[13] D. Simson, A. Skowro´nski, Elements of the representation theory of associative algebras, Vol. 2, Tubes and Concealed Algebras of Euclidean Type, London Mathematical Society Student Texts 71, Cambridge University Press, Cambridge, 2007.Search in Google Scholar

[14] Cs. Szántó, Hall numbers and the composition algebra of the Kronecker algebra, Algebr. Represent. Theory, 9 (2006), 465-495.10.1007/s10468-006-9019-0Search in Google Scholar

[15] Cs. Szántó, On the Hall product of preinjective Kronecker modules, Mathematica (Cluj), 48 (71), No. 2 (2006), 203-206.Search in Google Scholar

[16] Cs. Szántó, I. Szöllősi, On preprojective short exact sequences in the Kronecker case, J. Pure Appl. Algebra, 216 (2012), no. 5, 1171-1177.Search in Google Scholar

[17] Cs. Szántó, I. Szöllősi, Preinjective subfactors of preinjective Kronecker modules, arXiv:1309.4710 [math.RT], 13 September 2013, 13 pages.Search in Google Scholar

[18] Cs. Szántó, I. Szöllősi, The terms in the Ringel-Hall product of preinjective Kronecker modules, Period. Math. Hungar., 63 (2) (2011), 75-92.10.1007/s10998-011-8227-5Search in Google Scholar

[19] I. Szöllősi, Computing the extensions of preinjective and preprojective Kronecker modules, J. Algebra, 408 (2014) 205-221.Search in Google Scholar

[20] I. Szöllősi, The extension monoid product of preinjective Kronecker modules, Mathematica (Cluj), 55 (78), No. 1 (2013), 75-88. Search in Google Scholar