Twisted homology of symmetric groups

Author:
Stanislaw Betley

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3439-3445

MSC (1991):
Primary 20J06; Secondary 18G99

Published electronically:
July 2, 2002

MathSciNet review:
1918818

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the homology of symmetric groups with coefficients coming from the functor . We are primarily interested in the limit where . Our main goal is to compare the described above situation with the case of general linear groups.

**[B1]**Stanislaw Betley,*Calculations in 𝑇𝐻𝐻-theory*, J. Algebra**180**(1996), no. 2, 445–458. MR**1378539**, 10.1006/jabr.1996.0076**[B2]**Stanislaw Betley,*On stable 𝐾-theory with twisted coefficients*, Algebraic 𝐾-theory (Poznań, 1995) Contemp. Math., vol. 199, Amer. Math. Soc., Providence, RI, 1996, pp. 19–29. MR**1409615**, 10.1090/conm/199/02470**[B3]**Stanisław Betley,*Homology of 𝐺𝑙(𝑅) with coefficients in a functor of finite degree*, J. Algebra**150**(1992), no. 1, 73–86. MR**1174889**, 10.1016/S0021-8693(05)80050-X**[B4]**Stanisław Betley,*Stable derived functors, the Steenrod algebra and homological algebra in the category of functors*, Fund. Math.**168**(2001), no. 3, 279–293. MR**1853410**, 10.4064/fm168-3-4**[BP-1]**Stanisław Betley and Teimouraz Pirashvili,*Twisted (co)homological stability for monoids of endomorphisms*, Math. Ann.**295**(1993), no. 4, 709–720. MR**1214957**, 10.1007/BF01444912**[BP-2]**Stanisław Betley and Teimuraz Pirashvili,*Stable 𝐾-theory as a derived functor*, J. Pure Appl. Algebra**96**(1994), no. 3, 245–258. MR**1303284**, 10.1016/0022-4049(94)90101-5**[BS]**Stanislaw Betley and Jolanta Słomińska,*New approach to the groups 𝐻_{*}(Σ_{𝑛},𝐿𝑖𝑒_{𝑛}) by the homology theory of the category of functors*, J. Pure Appl. Algebra**161**(2001), no. 1-2, 31–43. MR**1834077**, 10.1016/S0022-4049(00)00094-3**[FFSS]**Vincent Franjou, Eric M. Friedlander, Alexander Scorichenko, and Andrei Suslin,*General linear and functor cohomology over finite fields*, Ann. of Math. (2)**150**(1999), no. 2, 663–728. MR**1726705**, 10.2307/121092**[JP]**Mamuka Jibladze and Teimuraz Pirashvili,*Cohomology of algebraic theories*, J. Algebra**137**(1991), no. 2, 253–296. MR**1094244**, 10.1016/0021-8693(91)90093-N**[vdK]**Wilberd van der Kallen,*Homology stability for linear groups*, Invent. Math.**60**(1980), no. 3, 269–295. MR**586429**, 10.1007/BF01390018**[K]**Christian Kassel,*Stabilisation de la 𝐾-théorie algébrique des espaces topologiques*, Ann. Sci. École Norm. Sup. (4)**16**(1983), no. 1, 123–149 (French). MR**719766****[N]**Minoru Nakaoka,*Decomposition theorem for homology groups of symmetric groups*, Ann. of Math. (2)**71**(1960), 16–42. MR**0112134****[P1]**Teimuraz Pirashvili,*Dold-Kan type theorem for Γ-groups*, Math. Ann.**318**(2000), no. 2, 277–298. MR**1795563**, 10.1007/s002080000120**[P2]**Teimuraz Pirashvili,*Hodge decomposition for higher order Hochschild homology*, Ann. Sci. École Norm. Sup. (4)**33**(2000), no. 2, 151–179 (English, with English and French summaries). MR**1755114**, 10.1016/S0012-9593(00)00107-5**[S]**A. Scorichenko. Stable K-theory and functor homology over a ring.*Preprint IAS, 2000*.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (1991):
20J06,
18G99

Retrieve articles in all journals with MSC (1991): 20J06, 18G99

Additional Information

**Stanislaw Betley**

Affiliation:
Instytut Matematyki, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Email:
betley@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-02-06763-1

Received by editor(s):
October 4, 2000

Published electronically:
July 2, 2002

Additional Notes:
The author was partially supported by the Polish Scientific Grant (KBN) 2 P03A 01113

Communicated by:
Ralph Cohen

Article copyright:
© Copyright 2002
American Mathematical Society