Mikola
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 Aug30 comment Which manifolds are parallelizable? Thanks, that makes this a lot more clear. Aug30 comment Which manifolds are parallelizable? What does $sk_1(X)$ mean? Jun7 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. Jun7 accepted Notation for a multiplicative algebra Jun6 answered A numerical inverse problem May25 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 ). Apr5 awarded Supporter Apr4 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. Apr4 awarded Scholar Apr4 accepted What is the motivation for the “Covering Homotopy Property” in a fibration? Apr4 awarded Student Apr4 answered Intersection of 2 spheres and a cube Apr4 asked What is the motivation for the “Covering Homotopy Property” in a fibration? Aug11 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... Aug9 revised Notation for a multiplicative algebra edited title Aug9 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. Aug9 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. Aug9 awarded Editor Aug9 revised Notation for a multiplicative algebra deleted 25 characters in body; added 44 characters in body Aug9 asked Notation for a multiplicative algebra