RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2009, Volume 15, Issue 8, Pages 3–93 (Mi fpm1282)

On the structure of a relatively free Grassmann algebra

A. V. Grishin, L. M. Tsybulya

Moscow State Pedagogical University

Abstract: We investigate the multiplicative and $T$-space structure of the relatively free algebra $F^{(3)}$ with a unity corresponding to the identity $[[x_1,x_2],x_3]=0$ over an infinite field of characteristic $p>0$. The highest emphasis is placed on unitary closed $T$-spaces over a field of characteristic $p>2$. We construct a diagram containing all basic $T$-spaces of the algebra $F^{(3)}$, which form infinite chains of the inclusions. One of the main results is the decomposition of quotient $T$-spaces connected with $F^{(3)}$ into a direct sum of simple components. Also, the studied $T$-spaces are commutative subalgebras of $F^{(3)}$; thus, the structure of $F^{(3)}$ and its subalgebras can be described as modules over these commutative algebras. Separately, we consider the specifics of the case $p=2$. In Appendix, we study nonunitary closed $T$-spaces and the case of a field of zero characteristic.

Full text: PDF file (798 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2010, 171:2, 149–212

Bibliographic databases:

UDC: 512.552

Citation: A. V. Grishin, L. M. Tsybulya, “On the structure of a relatively free Grassmann algebra”, Fundam. Prikl. Mat., 15:8 (2009), 3–93; J. Math. Sci., 171:2 (2010), 149–212

Citation in format AMSBIB
\Bibitem{GriTsy09} \by A.~V.~Grishin, L.~M.~Tsybulya \paper On the structure of a~relatively free Grassmann algebra \jour Fundam. Prikl. Mat. \yr 2009 \vol 15 \issue 8 \pages 3--93 \mathnet{http://mi.mathnet.ru/fpm1282} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2745014} \elib{http://elibrary.ru/item.asp?id=15340724} \transl \jour J. Math. Sci. \yr 2010 \vol 171 \issue 2 \pages 149--212 \crossref{https://doi.org/10.1007/s10958-010-0131-7} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78349313679} 

• http://mi.mathnet.ru/eng/fpm1282
• http://mi.mathnet.ru/eng/fpm/v15/i8/p3

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Grishin, “On the Center of a Relatively Free Lie-Nilpotent Algebra of Index $4$”, Math. Notes, 91:1 (2012), 139–140
2. A. V. Grishin, “On $T$-spaces in a relatively free two-generated Lie nilpotent associative algebra of index $4$”, J. Math. Sci., 191:5 (2013), 686–690
3. A. V. Grishin, S. V. Pchelintsev, “On centres of relatively free associative algebras with a Lie nilpotency identity”, Sb. Math., 206:11 (2015), 1610–1627
4. A. V. Grishin, “On the measure of inclusion in relatively free algebras with the identity of Lie nilpotency of degree 3 or 4”, Sb. Math., 210:2 (2019), 234–244
•  Number of views: This page: 219 Full text: 62 References: 24 First page: 1