| Title:
|
On some free semigroups, generated by matrices (English) |
| Author:
|
Słanina, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
289-299 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $$ A=\left [ \begin {matrix} 1 & 2 \\ 0 & 1 \end {matrix} \right ],\quad B_{\lambda }=\left [ \begin {matrix} 1 & 0 \\ \lambda & 1 \end {matrix} \right ]. $$ We call a complex number $\lambda $ “semigroup free“ if the semigroup generated by $A$ and $B_{\lambda }$ is free and “free” if the group generated by $A$ and $B_{\lambda }$ is free. First families of semigroup free $\lambda $'s were described by J. L. Brenner, A. Charnow (1978). In this paper we enlarge the set of known semigroup free $\lambda $'s. To do it, we use a new version of “Ping-Pong Lemma” for semigroups embeddable in groups. At the end we present most of the known results related to semigroup free and free numbers in a common picture. (English) |
| Keyword:
|
free semigroup |
| Keyword:
|
semigroup of matrices |
| MSC:
|
15A30 |
| MSC:
|
20E05 |
| MSC:
|
20M05 |
| idZBL:
|
Zbl 06486946 |
| idMR:
|
MR3360426 |
| DOI:
|
10.1007/s10587-015-0175-4 |
| . |
| Date available:
|
2015-06-16T17:29:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144268 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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