All Questions
Tagged with nonassociative-algebra or non-associative-algebras
59 questions
1
vote
0
answers
76
views
What is the operator norm of the sedenions and beyond?
Suppose that $K$ is a field. Then for all $n$, define a bilinear operation $*$ (or $*_{n,K}$ in case there may be ambiguity) on $K^{2^n}$ along with a conjugation operation $^*$ on $K^{2^n}$ by ...
1
vote
0
answers
35
views
An algebraic characterization of dual translation projective planes
It is well-known that translation projective planes are coordinatized by quasifields. More precisely, a projective plane is translation if and only if it has a ternary-ring $R$ which is linear, the ...
- 41.8k
1
vote
0
answers
32
views
Is the (left or right) Bol property Isotopy-invariant?
It is well known that a loop satisfies both the left Bol property $(x(yx))z = x(y(xz))$ and the right Bol property $((zx)y)x = z((xy)x)$ if and only if it is a Moufang loop. It is also well known that ...
- 1,947
1
vote
0
answers
166
views
Nonassociative algebras closed under $\sqrt{\ }$?
Consider a non-associative commutative unital algebra of finite dimension where the product is defined by a Cayley table such that elements are generated with real number coefficients
$(a_0, \dotsc, ...
- 763
1
vote
0
answers
50
views
Separable nonassociative algebras
In his paper "Structure and Representation of Nonassociative Algebras", Schafer notes that an arbitrary nonassociative algebra over a field is separable "if and only if the ...
- 323
0
votes
0
answers
46
views
Nonassociativity in Cayley-Algebras
Let $(E,s)$ be a Cayley algebra over a unital commutative ring $A$ with unit element $e$ and $s$ an antiautomorphism (i.e. $s(uv) = s(v)s(u)$, $u,v \in E$) of $E$ such that $u + s(u) \in Ae$ and $N(u) ...
- 2,101
0
votes
0
answers
172
views
When does this commutative non-associative algebra have nilpotent elements?
Consider a non-associative commutative unital algebra of finite dimension where the product is defined by a Cayley table such that elements are generated with real number coefficients
$(a_0, \dotsc, ...
- 763
0
votes
0
answers
125
views
A question about index of the commutant in a Moufang loop
Let $M$ be a non-commutative Moufang loop and $C(M)$ be its commutant. I can prove that the index of $C(M)$ in $M$, $|M:C(M)|$, is greater than or equal to 4. Also, I can show that $|M:Z(M)|\geq 4$, ...
- 123
-2
votes
1
answer
560
views
Non-associative module theory [closed]
I'm looking for a reference that treats basic module theory over non-associative rings, the isomorphism theorems and so on. I imagine the theory is known, but have not been able to find a reference.
...
- 1