- Précédent

- Feuilleter

- Série 6 : Tome 25 (2016)

- no. 2-3

- p. 363-384

- Suivant

- Abstract (VO)

- Résumé

In his extension [3] of W. Siegel’s ideas on string quantization, N. Berkovits made several observations which deserve further study and development. Indeed, interesting accounts of this work have already appeared in the mathematical literature [8, 15] and in a different guise due to L. Avramov. In this paper we bridge between these three approaches, by providing a complex that is useful in the calculation of some homologies.

En étendant des idées de W.Siegel sur la quantisation des cordes, N. Berkovits [3] a fait quelques remarques qui méritent d’être étudiées et développées. En fait, des rapports intéressants sur ce travail sont déjà parus dans la littérature mathématique [8, 15], liés aussi à une contruction due à L. Avramov. Dans cet article, on tend des ponts entre ces trois approches, en utilisant la construction d’un complexe approprié au calcul de certains groupes d’homologie.

- Détail

- Export

- Comment citer

Imma Gálvez 1 ; Vassily Gorbounov 2 ; Zain Shaikh 3 ; Andrew Tonks 4

- BibTeX

- RIS

- EndNote

- Bibliographie

- Cité par

[1] Avramov (L.L.).— Free Lie subalgebras of the cohomology of local rings Trans. Amer. Math. Soc. 270, no. 2, p. 589-608 (1982). | DOI | Zbl | MR

[2] Avramov (L.L.).— Infinite free resolutions. Six lectures on commutative algebra Progr. Math., 166, p. 1-118, Birkhäuser, Basel (1998). | DOI | Zbl

[3] Berkovits (N.).— Cohomology in the pure spinor formalism for the superstring, J. High Energy Phys. 9 (2000). | DOI | MR

[4] Bourbaki (N.).— Lie Groups and Lie Algebras, Chapters 1-3, Springer (1991).

[5] Chevalley (C.); Eilenberg (S.).— Cohomology Theory of Lie Groups and Lie Algebras Trans. Amer. Math. Soc. 63 p. 85-124 (1948). | DOI | MR

[6] Eisenbud (D.).— Commutative Algebra with a View Toward Algebraic Geometry, Grad. Text. in Math. Springer-Verlag, 1995. xvi+785 pp. | Zbl

[7] Gauss (C.).— Disquisitiones generales de congruentis, Analysis residuorum. Caput octavum, Collected Works, Vol. 2, Georg Olms Verlag, Hildersheim, New York, p. 212-242 (1973). | DOI

[8] Gorodentsev (A.); Khoroshkin (A.); Rudakov (A.).— On syzygies of highest weight orbits, Amer. Math. Soc. Transl. 221 (2007). | DOI

[9] Gross (B. H.); Wallach (N. R.).— On the Hilbert polynomials and Hilbert series of homogeneous projective varieties, In: Arithmetic geometry and automorphic forms, Adv. Lect. Math. 19 p. 253-263 (2011).

[10] Hess (K.).— Rational homotopy theory: a brief introduction. Interactions between homotopy theory and algebra, 175–202, Contemp. Math., 436, Amer. Math. Soc., Providence, RI ( 2007). | DOI | Zbl

[11] Herscovich (E.); Solotar (A.).— Representations of Yang-Mills algebras, Annals of Mathematics 173, p. 1043-1080 (2011). | DOI | Zbl | MR

[12] Kadeishvili (T.).— The algebraic structure in the homology of an A(∞)-algebra (Russian), Soobshch. Akad. Nauk Gruzin. SSR 108 p. 249-252 (1982).

[13] Kang (S.-J.).— Graded Lie Superalgebras and the Superdimension Formula, Journal of Algebra 204, p. 597-655 (1998). | DOI | Zbl | MR

[14] MacLane (S.).— Homology, Reprint of the 1975 edition, Springer-Verlag, Berlin, 1995. x+422 pp.

[15] Movshev (M.); Schwarz (A.).— Algebraic structure of Yang-Mills theory, in The Unity of Mathematics: In Honor of the Ninetieth Birthday of I.M. Gelfand (Progress in Mathematics 244) Birkhäuser p. 473-523 (2006). | DOI

[16] Polishchuk (A.); Positselski (L.).— Quadratic algebras, University Lecture Series, 37. AMS, (2005). xii+159 pp. | DOI

[17] Quillen (D.).— Rational homotopy theory, Ann. of Math. (2) 90 p. 205-295 (1969). | DOI | Zbl | MR

[18] Sullivan (D.).— Infinitesimal computations in topology, Publications Mathématiques de l’IHÉS, 47 p. 269-331 (1977). | DOI

Cité par Sources :