Timeline for Algebraic axiomatization for AB+BA^T operation on matrices
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2023 at 15:33 | history | edited | darij grinberg | CC BY-SA 4.0 |
maybe an edit will fix the kitty bug
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| Aug 23, 2011 at 11:01 | comment | added | Pasha Zusmanovich | @Qiaochu: A fruitful approach to identities of algebras is first to superize the situation (by injecting signs appropriately) and then go back from superalgebras to algebras via the Grassmann envelope. Maybe this approach may help when considering identities of algebras in the signature (binary multiplication, $\square$). | |
| Aug 19, 2011 at 10:54 | comment | added | Pasha Zusmanovich | @probably: Ok, yes, that's true. | |
| Aug 17, 2011 at 12:41 | comment | added | probably | Matrix algebras with operation $\Box$ from the initial question are nonassociative, therefore if there are no identities then this variety will contain absolutely free nonassociative algebra? | |
| Aug 17, 2011 at 12:15 | comment | added | Pasha Zusmanovich | @probably: It will contain an absolutely free associative algebra (as all algebras generating the variety are associative). | |
| Aug 17, 2011 at 12:07 | comment | added | probably | Therefore variety generated by matrix algebras from the initial question will contain an absolutely free nonassociative algebra? | |
| Aug 8, 2011 at 19:06 | comment | added | Pasha Zusmanovich | I don't know. Sure, this argument is valid only when we consider identitites in $\square$ only. | |
| Aug 8, 2011 at 18:48 | comment | added | Qiaochu Yuan | What can we say if we include the transpose as a basic operation? For example, we now have the identity $(a \Box b)^T = a b^T + b^T a^T = a \Box (b^T)$. | |
| Aug 8, 2011 at 18:18 | history | answered | Pasha Zusmanovich | CC BY-SA 3.0 |