# Is the Bruhat cell Zariski open in a connected algebraic group $G$? [closed]

Is the Bruhat cell Zariski-open in a connected algebraic group $$G$$? Specifically, is the big Bruhat cell Zariski-open (and maybe Zariski-dense)?

Is it true for all the Bruhat cells?

## closed as off-topic by abx, LSpice, SashaP, user44191, Dima PasechnikJul 12 at 21:13

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• The top dimensional Bruhat cell is Zarisli open and dense; and, of course, all the others cells are not. You will find this in any book on algebraic groups, e.g. Linear Algebraic Groups by A. Borel. – abx Jul 8 at 15:58
• Zariski open implies Zariski dense in a connected algebraic group. – LSpice Jul 9 at 20:57