Differentiation algorithm and classification of representations

A. G. Zavadskii

Izvestiya. Mathematics , Tome 39 (1992) no. 2, pp. 975-1012.

Résumé

A complete classification of the indecomposable representations of partially ordered sets of finite growth is given.

Bibliographie

[1] Auslander M., Reiten I., “Representation theory of artin algebras. III. IV”, Comm. Algebra, 1975, no. 3, 239–294 ; 1977, no. 5, 443–518 | DOI | MR | Zbl | DOI | MR | Zbl

[2] Bondarenko V. M., Zavadskii A. G., Nazarova L. A., “O predstavleniyakh ruchnykh chastichno uporyadochennykh mnozhestv”, Predstavleniya i kvadratichnye formy, In-t matematiki AN USSR, Kiev, 1979, 75–106 | MR

[3] Bünermann D., Auslander–Reiten Köcher von einparametrigen teilweise geordneten Mengen, Dissertation, Düsseldorf, 1981

[4] Dlab V., Ringel C. M., “Indecomposable representations of graphs and algebras”, Memoires Amer. Math. Soc., 173 (1976) | MR | Zbl

[5] Drozd Yu. A ., “Preobrazovaniya Kokstera i predstavleniya chastichno uporyadochennykh mnozhestv”, Funkts. analiz i ego prilozh., 8 (1974), 34–42 | MR | Zbl

[6] Gabriel P., “Représentations indécomposables des ensembles ordonnés”, Sem. Dubreil (algebra) (1972–73), 13, 1973, 1301–1304 | MR

[7] Gelfand I. M., Ponomarev V. A., “Problems of linear algebra and classification of quadruples of subspaces in a finite-dimentional vector space”, Hilbert space operators and operator algebras (Proc. Internat. Conf., Tihany, 1970), North-Holland, Amsterdam, 1972, 163–237 | MR

[8] Kholl M., Kombinatorika, Mir, M., 1970 | MR

[9] Kleiner M. M., “Chastichno uporyadochennye mnozhestva konechnogo tipa”, Zap. nauchn. sem. LOMI, 28, 1972, 32–41 | MR | Zbl

[10] Kleiner M. M., “O tochnykh predstavleniyakh chastichno uporyadochennykh mnozhestv konechnogo tipa”, Zap. nauchn. sem. LOMI, 28, 1972, 42–59 | MR

[11] Kleiner M. M., Roiter A. V., “Predstavleniya differentsialnykh graduirovannykh kategorii”, Matrichnye zadachi, In-t matematiki AN USSR, Kiev, 1977, 5–70 | MR | Zbl

[12] Nazarova L. A., “Predstavleniya chetveriady”, Izv. AN SSSR. Ser. matem., 31:6 (1967), 1361–1377 | MR

[13] Nazarova L. A., “Predstavleniya kolchanov beskonechnogo tipa”, Izv. AN SSSR. Ser. matem., 37:4 (1973), 752–791 | MR | Zbl

[14] Nazarova L. A., “Chastichno uporyadochennye mnozhestva beskonechnogo tipa”, Izv. AN SSSR. Ser. matem., 39:5 (1975), 963–991 | MR | Zbl

[15] Nazarova L. A., Roiter A. V., “Predstavleniya chastichno uporyadochennykh mnozhestv”, Zap. nauchn. sem. LOMI, 28, 1972, 5–31 | MR | Zbl

[16] Nazarova L. A., Roiter A. V., “Ob odnoi zadache I. M. Gelfanda”, Funkts. analiz i ego prilozh., 7 (1973), 54–69 | MR | Zbl

[17] Otrashevskaya V. V., “O predstavleniyakh odnoparametricheskikh chastichno uporyadochennykh mnozhestv”, Matrichnye zadachi, In-t matematiki AN USSR, Kiev, 1977, 144–149 | Zbl

[18] Ovsienko S. A., Roiter A. V., “Bilineinye formy i kategorii predstavlenii”, Matrichnye zadachi, In-t matematiki AN USSR, Kiev, 1977, 71–80 | MR | Zbl

[19] Ringel C. M., “On algorithms for solving vector space problems. II. Tame algebras”, Representation theory. I (Proc. Workshop, Carleton Univ., Ottawa, Ont., 1979), Lecture Notes in Math., 831, Springer, Berlin, 1980, 137–287 | MR

[20] Ringel C. M., Tame algebras and integral quadratic forms, Lecture Notes in Mathematics, 1099, Springer-Verlag, Berlin, 1984, 376 pp. | MR | Zbl

[21] Roiter A. V., “Matrichnye zadachi i predstavleniya boksov”, Predstavleniya i kvadratichnye formy, In-t matematiki AN USSR, Kiev, 1979, 3–38 | MR

[22] Simson D., “On vector spase categories and differentiations of right peak rings”, Proc. ICRA–IV, Carleton–Ottawa Math. Lect. Notes Ser., 1984, 31.01–31.17

[23] Zavadskii A. G., “Differentsirovanie po pare tochek”, Matrichnye zadachi, In-t matematiki AN USSR, Kiev, 1977, 115–121 | MR | Zbl

[24] Zavadskii A. G., Serii predstavlenii i forma Titsa, Preprint In-ta matematiki AN USSR No 81.27, Kiev, 1981, 3–20

[25] Zavadskii A. G., Tochnye chastichno uporyadochennye mnozhestva konechnogo rosta, Preprint In-ta matematiki AN USSR No 81.27, Kiev, 1981, 30–42 | MR

[26] Zavadskii A. G., Predstavleniya chastichno uporyadochennykh mnozhestv konechnogo rosta, Dep. UkrNIINTI No 413 Uk–D83, Kiev, 1983, 76 pp. | Zbl

[27] Zavadskii A. G., “Stroenie predstavlenii chastichno uporyadochennykh mnozhestv konechnogo rosta”, Lineinaya algebra i teoriya predstavlenii, In-t matematiki AN USSR, Kiev, 1983, 55–67 | MR

[28] Zavadskij A. G., “Classification of representations of posets of finite growth”, Proc. ICRA–IV, Carleton–Ottawa Math. Lect. Notes Ser., 1984, 36.01–30.15

[29] Zavadskii A. G., Algoritm differentsirovaniya i klassifikatsiya predstavlenii, Dep. UkrNIINTI No 1606 Uk–87, Kiev, 1987, 129 pp.

[30] Zavadskii A. G., Nazarova L. A., “Chastichno uporyadochennye mnozhestva ruchnogo tipa”, Matrichnye zadachi, In-t matematiki AN USSR, Kiev, 1977, 122–143 | MR | Zbl

[31] Zavadskii A. G., Nazarova L. A., O konechnosti i ogranichennosti chisla parametrov, Preprint In-ta matematiki AN USSR No 81.27, Kiev, 1981, 21–29 | MR

[32] Zavadskii A. G., Nazarova L. A., “Chastichno uporyadochennye mnozhestva konechnogo rosta”, Funkts. analiz i ego prilozh., 16:2 (1982), 72–73 | MR | Zbl