On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers
In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of...
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| Datum: | 1995 |
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| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511689608265728 |
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| author | Tushev, A. V. Тушев, А. В. Тушев, А. В. |
| author_facet | Tushev, A. V. Тушев, А. В. Тушев, А. В. |
| author_sort | Tushev, A. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:59:28Z |
| description | In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of $A$ that maps $x,y$ into $a_x, b_y$, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.” |
| first_indexed | 2026-03-24T03:16:53Z |
| format | Article |
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| id | umjimathkievua-article-5460 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
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| language | rus English |
| last_indexed | 2026-03-24T03:16:53Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/70/a50c17d643932a817b801025a597f170.pdf |
| spelling | umjimathkievua-article-54602020-03-19T08:59:28Z On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers Об идеалах групповой алгебры свободной группы степени свободы 2 над полем комплексных чисел Tushev, A. V. Тушев, А. В. Тушев, А. В. In this paper, we prove the existence of an elementα of the group algebra $A=ℂF$ of a free group $F$ with two generatorsx andy over the field of complex numbers $C$ such that, for any complex $a$ and $b$ for which $¦a¦=¦b¦=1$, we have $A ∩ ϑ_{a,b} (α)A=0$, where $ϑ_{a,b}$ ($α$ is an automorphism of $A$ that maps $x,y$ into $a_x, b_y$, respectively. Thus, we give a negative answer to question 12.46 of P. A. Linnel from “Kourovka Notebook.” Доведено, що в груповій алгебрі $A=ℂF$ вільної групи $F$ з двома твірними $х, у$ над полем комплексних чисел $C$ існує такий елемент $a$, що для будь-яких комплексних чисел $a, b$ з модулем 1 перетин ідеалів $¦a¦=¦b¦=1$ нульовий, де $α$—автоморфізм алгебри $A$, який переводить $х, у$ в $а_х, b_y$ відповідно. Тим самим дана негативна відповідь на запитання П. Ліннела з "Коурівського зошита". Institute of Mathematics, NAS of Ukraine 1995-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5460 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 4 (1995); 571-572 Український математичний журнал; Том 47 № 4 (1995); 571-572 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5460/7609 https://umj.imath.kiev.ua/index.php/umj/article/view/5460/7610 Copyright (c) 1995 Tushev A. V. |
| spellingShingle | Tushev, A. V. Тушев, А. В. Тушев, А. В. On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title | On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title_alt | Об идеалах групповой алгебры свободной группы степени свободы 2 над
полем комплексных чисел |
| title_full | On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title_fullStr | On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title_full_unstemmed | On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title_short | On ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| title_sort | on ideals of the group algebra of a free group of degree of freedom two over the field of complex numbers |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5460 |
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