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Aug
30
comment Which manifolds are parallelizable?
Thanks, that makes this a lot more clear.
Aug
30
comment Which manifolds are parallelizable?
What does $sk_1(X)$ mean?
Jun
7
comment Notation for a multiplicative algebra
Well, it has been almost a year since I asked this question and I have maybe learned a bit since then. I now would tend to agree that it is better to explicitly write out the product, since that makes the most sense for finite groups and generalizes readily to the non-commutative case.
Jun
7
accepted Notation for a multiplicative algebra
Jun
6
answered A numerical inverse problem
May
25
comment Outer product of a vector with itself
The outer product of any vector with itself is always 0, since the outer product is skew symmetric. (EDIT: I would have made this a comment, but I don't have enough rep to do so on this stack exchange site ).
Apr
5
awarded  Supporter
Apr
4
comment What is the motivation for the “Covering Homotopy Property” in a fibration?
Thank you, your post cleared a lot up for me (I would give you an upvote, but I don't have enough karma). I think I understand how this works, but I am still uncertain exactly what this property is good for. I am guessing that it has something to do with wanting to be able to decompose spaces over short exact sequences/extensions, like is done in group theory, but this concept is a bit hazy still. I will think about it a bit more.
Apr
4
awarded  Scholar
Apr
4
accepted What is the motivation for the “Covering Homotopy Property” in a fibration?
Apr
4
awarded  Student
Apr
4
answered Intersection of 2 spheres and a cube
Apr
4
asked What is the motivation for the “Covering Homotopy Property” in a fibration?
Aug
11
comment Notation for a multiplicative algebra
MattE: I don't understand what is unclear. I don't think you can form matrix algebras on spaces which do not have a basis (operator algebras on the other hand are a different story). Also I explicitly said n x n matrices, so I don't know where you got the idea that things could be infinite rank...
Aug
9
revised Notation for a multiplicative algebra
edited title
Aug
9
comment Notation for a multiplicative algebra
And actually I just thought of another situation which is even worse. Consider the module of n x n matrices. Then there are at least 3 (!!!) distinct algebras: 1. The matrix algebra, with product given by matrix multiplication. 2. The multiplicative algebra, with the Hadamard product. 3. A Lie algebra, with the Lie bracket as the underlying operator.
Aug
9
comment Notation for a multiplicative algebra
Hmm... Is it maybe too ambiguous? Another place where this also gets used is in the Banach algebra of multipliers, where I have seen people write $M(G)$ for locally compact abelian groups. However this fixes the underlying ring to be $\mathbb C$ and brings in a whole bunch of extra assumptions I really don't need.
Aug
9
awarded  Editor
Aug
9
revised Notation for a multiplicative algebra
deleted 25 characters in body; added 44 characters in body
Aug
9
asked Notation for a multiplicative algebra