Ring $R_{ 152 }$

$C\ell_{2,1}(\mathbb R)$: the geometric algebra of Minkowski 3-space


The Clifford algebra of a $3$ dimensional $\mathbb R$ vector space with bilinear form having signature $(+1,+1,-1)$. This algebra is isomorphic to $M_2(\mathbb R)\times M_2(\mathbb R)$. In addition to being viewed as a "geometric algebra" for the space, it can also be viewed as the "conformal geometric algebra" for a $1$ dimensional real vector space.

Keywords Clifford algebra direct product matrix ring


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  • Legend
    • = has the property
    • = does not have the property
    • = information not in database
    Name Measure
    composition length left: 4right: 4
    global dimension left: 0right: 0
    Krull dimension (classical) 0
    uniform dimension left: 4right: 4
    weak global dimension 0
    Name Description
    Jacobson radical $\{0\}$
    Left singular ideal $\{0\}$
    Left socle $R$
    Right singular ideal $\{0\}$
    Right socle $R$