Coordinates of maximal roots of weakly non-negative unit forms

P. Dräxler; N. Golovachtchuk; S. Ovsienko; J. de la Pena

Colloquium Mathematicae (1998)

  • Volume: 78, Issue: 2, page 163-193
  • ISSN: 0010-1354

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Dräxler, P., et al. "Coordinates of maximal roots of weakly non-negative unit forms." Colloquium Mathematicae 78.2 (1998): 163-193. <http://eudml.org/doc/210609>.

@article{Dräxler1998,
author = {Dräxler, P., Golovachtchuk, N., Ovsienko, S., de la Pena, J.},
journal = {Colloquium Mathematicae},
keywords = {positive roots; tame algebras; quadratic forms; weakly nonnegative unit forms; Euler characteristics; roots; Euler forms; representation types; directing modules; path algebras},
language = {eng},
number = {2},
pages = {163-193},
title = {Coordinates of maximal roots of weakly non-negative unit forms},
url = {http://eudml.org/doc/210609},
volume = {78},
year = {1998},
}

TY - JOUR
AU - Dräxler, P.
AU - Golovachtchuk, N.
AU - Ovsienko, S.
AU - de la Pena, J.
TI - Coordinates of maximal roots of weakly non-negative unit forms
JO - Colloquium Mathematicae
PY - 1998
VL - 78
IS - 2
SP - 163
EP - 193
LA - eng
KW - positive roots; tame algebras; quadratic forms; weakly nonnegative unit forms; Euler characteristics; roots; Euler forms; representation types; directing modules; path algebras
UR - http://eudml.org/doc/210609
ER -

References

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  1. [Bo] K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. (2) 28 (1983), 461-469. Zbl0532.16020
  2. [BG] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378. Zbl0482.16026
  3. [DP] A. Dean and J. A. de la Pena, Algorithms for weakly non-negative quadratic forms, Linear Algebra Appl. 235 (1996), 35-46. Zbl0848.65031
  4. [D-Z] P. Dräxler, Yu. A. Drozd, N. S. Golovachtchuk, S. A. Ovsienko and M. M. Zeldych, Towards classification of sincere weakly positive unit forms, European J. Combin. 16 (1995), 1-16. Zbl0830.16013
  5. [Ga] P. Gabriel, Unzerlegbare Darstellungen I, Manuscripta Math. 6 (1972), 71-103. Zbl0232.08001
  6. [HP] D. Happel and J. A. de la Pena, Quadratic forms with a maximal sincere root, in: CMS Conf. Proc. 18, Amer. Math. Soc., 1996, 307-315. Zbl0857.16018
  7. [Hu] J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Grad. Texts in Math. 9, Springer, New York, 1990. 
  8. [Ka] V. G. Kac, Infinite Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge, 1972. 
  9. [Ov1] S. Ovsienko, Integral weakly positive forms, in: Schur Matrix Problems and Quadratic Forms, Kiev, 1978, 3-17. 
  10. [Ov2] S. Ovsienko, Maximal roots of sincere weakly nonnegative forms, lecture at the workshop on Quadratic Forms in the Representation Theory of Finite-Dimensional Algebras, Bielefeld, November 9-12, 1995. 
  11. [Pe1] J. A. de la Pena, On the representation type of one point extensions of tame concealed algebras, Manuscripta Math. 61 (1988), 183-194. Zbl0647.16021
  12. [Pe2] J. A. de la Pena, Algebras with hypercritical Tits form, in: Topics in Algebra, Banach Center Publ. 26, part I, PWN, Warszawa, 1990, 353-369. 
  13. [Pe3] J. A. de la Pena, Tame algebras with sincere directing modules, J. Algebra 161 (1993), 171-185. Zbl0808.16018
  14. [Pe4] J. A. de la Pena, The families of two-parametric tame algebras with sincere directing modules, in: CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 361-392. Zbl0799.16016
  15. [Ri] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984. 
  16. [Si] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon and Breach, 1992. Zbl0818.16009
  17. [Sl] P. Slodowy, Beyond Kac-Moody algebras, and inside, in: Lie Algebras and Related Topics, CMS Conf. Proc. 5, Amer. Math. Soc., 1986, 361-370. 
  18. [Za] A. G. Zavadskiĭ, Sincere partially ordered sets of finite growth, in: Mat. Inst. Akad. Nauk USSR, preprint 81.27, Kiev, 1981, 30-42 (in Russian). 

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